Schema-protected Multi Client Database

I am currently building an application that will host multiple clients in the same database. Each client will have their own schema. Common data will be stored in [dbo] tables commonly accessible. Client data will be stored in matching schema-specific tables.
EX:

[ClientA].[Orders] ...
[ClientB].[Orders] ...
[ClientC].[Orders] ...


So far so good.
Upon issuing select statements under the various logins, the proper table is accessed and improper tables are protected.

The problem comes when working with the various stored procs to access the data.
My original though was that I would have one version of the stored procs and they would be calling-schema aware, much like select statements are, and deal with the proper table data. What seems to be the case is that each client needs its own copy of ALL the stored procs, creating a maintenance nightmare considering each client's procs is identical in EVERY SINGLE WAY except for the owning schema.

It seems once a proc is called the ownership chain changes to the proc's schema and ignores the caller from there on out. Am I missing a step in this or do I have the proper understanding (and problem).

Example:

Attached is a sample database script.
Four (matching) tables. Stored proc for accessing data via a table function. Three logins dealing with various iterations:

login: clienta
setup: Entry point proc set, table function missing (will call dbo version)
result: Permission error on call to table function. Fix that and pulls data from dbo table

login: clientb

setup: Entry point proc using dbo, schema-specific table function set

result: Calls dbo version of function (not schema version) and pulls dbo table data

login: clientc

setup: Entry point proc set, table function set

result: Correct data pulled from schema table


login: db owner login

setup: Both dbo proc and dbo function set

result: DBO table data pulled


======================================================

-- ====================================================================
--
-- Create Database SchemaTest
--
-- ====================================================================

CREATE DATABASE SchemaTest
GO
USE SchemaTest
GO

-- ====================================================================
--
-- Create Users and Schemas
--
-- ====================================================================

IF NOT EXISTS (SELECT * FROM sys.database_principals WHERE name = N'clienta')
CREATE USER [clienta] FOR LOGIN [clienta] WITH DEFAULT_SCHEMA=[ClientA]
GO
IF NOT EXISTS (SELECT * FROM sys.database_principals WHERE name = N'clientb')
CREATE USER [clientb] FOR LOGIN [clientb] WITH DEFAULT_SCHEMA=[ClientB]
GO
IF NOT EXISTS (SELECT * FROM sys.database_principals WHERE name = N'clientc')
CREATE USER [clientc] FOR LOGIN [clientc] WITH DEFAULT_SCHEMA=[ClientC]
GO


IF NOT EXISTS (SELECT * FROM sys.schemas WHERE name = N'ClientA')
EXEC sys.sp_executesql N'CREATE SCHEMA [ClientA] AUTHORIZATION [clienta]'
GO

IF NOT EXISTS (SELECT * FROM sys.schemas WHERE name = N'ClientB')
EXEC sys.sp_executesql N'CREATE SCHEMA [ClientB] AUTHORIZATION [dbo]'
GO


IF NOT EXISTS (SELECT * FROM sys.schemas WHERE name = N'ClientC')
EXEC sys.sp_executesql N'CREATE SCHEMA [ClientC] AUTHORIZATION [dbo]'
GO






-- ====================================================================
--
-- Create Tables SType for each Schema
--
-- ====================================================================


SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientA].[SType]') AND type in (N'U'))
BEGIN
CREATE TABLE [ClientA].[SType](
[TypeID] [int] IDENTITY(1,1) NOT NULL,
[Text] [varchar](50) NOT NULL,
[Description] [varchar](100) NULL,
CONSTRAINT [PK_Type] PRIMARY KEY CLUSTERED
(
[TypeID] ASC
)WITH (PAD_INDEX = OFF, IGNORE_DUP_KEY = OFF) ON [PRIMARY]
) ON [PRIMARY]
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientB].[SType]') AND type in (N'U'))
BEGIN
CREATE TABLE [ClientB].[SType](
[TypeID] [int] IDENTITY(1,1) NOT NULL,
[Text] [varchar](50) NOT NULL,
[Description] [varchar](100) NULL,
CONSTRAINT [PK_Type] PRIMARY KEY CLUSTERED
(
[TypeID] ASC
)WITH (PAD_INDEX = OFF, IGNORE_DUP_KEY = OFF) ON [PRIMARY]
) ON [PRIMARY]
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientC].[SType]') AND type in (N'U'))
BEGIN
CREATE TABLE [ClientC].[SType](
[TypeID] [int] IDENTITY(1,1) NOT NULL,
[Text] [varchar](50) NOT NULL,
[Description] [varchar](100) NULL,
CONSTRAINT [PK_Type] PRIMARY KEY CLUSTERED
(
[TypeID] ASC
)WITH (PAD_INDEX = OFF, IGNORE_DUP_KEY = OFF) ON [PRIMARY]
) ON [PRIMARY]
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[SType]') AND type in (N'U'))
BEGIN
CREATE TABLE [dbo].[SType](
[TypeID] [int] IDENTITY(1,1) NOT NULL,
[Text] [varchar](50) NOT NULL,
[Description] [varchar](100) NULL,
CONSTRAINT [PK_Type] PRIMARY KEY CLUSTERED
(
[TypeID] ASC
)WITH (PAD_INDEX = OFF, IGNORE_DUP_KEY = OFF) ON [PRIMARY]
) ON [PRIMARY]
END
GO

-- ========================================================
-- Insert Sample Data
--
-- ========================================================
INSERT INTO [ClientA].[SType]
([Text])
VALUES ('A Data')

INSERT INTO [ClientB].[SType]
([Text])
VALUES ('B Data')

INSERT INTO [ClientC].[SType]
([Text])
VALUES ('C Data')

INSERT INTO [dbo].[SType]
([Text])
VALUES ('dbo Master Data')

GO







-- ====================================================================
--
-- Create proc GimmeTable for each Schema
--
-- ClientA has version
-- ClientB does not have version (will use dbo version)
-- ClientC has version
--
-- ====================================================================

GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[GimmeTable]') AND type in (N'P', N'PC'))
BEGIN
EXEC dbo.sp_executesql @statement = N'-- =============================================
-- Author: <Author,,Name>
-- Create date: <Create Date,,>
-- Description: <Description,,>
-- =============================================
CREATE PROCEDURE [dbo].[GimmeTable]
AS
BEGIN
SELECT * from tableSType()
END

'
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientA].[GimmeTable]') AND type in (N'P', N'PC'))
BEGIN
EXEC dbo.sp_executesql @statement = N'-- =============================================
-- Author: <Author,,Name>
-- Create date: <Create Date,,>
-- Description: <Description,,>
-- =============================================
CREATE PROCEDURE [ClientA].[GimmeTable]
AS
BEGIN
SELECT * from tableSType()
END

'
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientC].[GimmeTable]') AND type in (N'P', N'PC'))
BEGIN
EXEC dbo.sp_executesql @statement = N'-- =============================================
-- Author: <Author,,Name>
-- Create date: <Create Date,,>
-- Description: <Description,,>
-- =============================================
create PROCEDURE [ClientC].[GimmeTable]
AS
BEGIN
SELECT * from tableSType()
END


'
END
GO


-- ====================================================================
--
-- Create table function tableSType() for each Schema
--
-- ClientA does not have version (will use dbo version)
-- ClientB has version
-- ClientC has version
--
-- ====================================================================

SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientB].[tableSType]') AND type in (N'FN', N'IF', N'TF', N'FS', N'FT'))
BEGIN
execute dbo.sp_executesql @statement = N'-- =============================================
-- Author: <Author,,Name>
-- Create date: <Create Date,,>
-- Description: <Description,,>
-- =============================================
CREATE FUNCTION [ClientB].[tableSType]
()
RETURNS TABLE
AS
RETURN
(
select * from SType
)
'
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[ClientC].[tableSType]') AND type in (N'FN', N'IF', N'TF', N'FS', N'FT'))
BEGIN
execute dbo.sp_executesql @statement = N'-- =============================================
-- Author: <Author,,Name>
-- Create date: <Create Date,,>
-- Description: <Description,,>
-- =============================================
CREATE FUNCTION [ClientC].[tableSType]
()
RETURNS TABLE
AS
RETURN
(
select * from SType
)
'
END
GO
SET ANSI_NULLS ON
GO
SET QUOTED_IDENTIFIER ON
GO
IF NOT EXISTS (SELECT * FROM sys.objects WHERE object_id = OBJECT_ID(N'[dbo].[tableSType]') AND type in (N'FN', N'IF', N'TF', N'FS', N'FT'))
BEGIN
execute dbo.sp_executesql @statement = N'-- =============================================
-- Author: <Author,,Name>
-- Create date: <Create Date,,>
-- Description: <Description,,>
-- =============================================
create FUNCTION [dbo].[tableSType]
()
RETURNS TABLE
AS
RETURN
(
select * from SType
)

'
END




-- ====================================================================
--
-- Set permissions on GimmeTable to public
--
-- ====================================================================

GRANT EXEC ON [dbo].[GimmeTable] TO PUBLIC
GRANT EXEC ON [ClientA].[GimmeTable] TO PUBLIC
GRANT EXEC ON [ClientC].[GimmeTable] TO PUBLIC

GRANT SELECT ON [dbo].[SType] TO PUBLIC
GRANT SELECT ON [ClientA].[SType] TO PUBLIC
GRANT SELECT ON [ClientB].[SType] TO PUBLIC
GRANT SELECT ON [ClientC].[SType] TO PUBLIC

GO






-- ====================================================================
--
-- Use these statements with each user and compare results
--
-- ====================================================================


EXEC GimmeTable
select * from SType