Permissions With Dynamic SQL Within Stored Procedure

Okay, I have sort of a peculiar permissions question I am wondering if someone can help me with. Basically, here's the scenario...

I have a CLR stored procedure which does some dynamic SQL building based on values sent in via XML. It's a CLR stored procedure using XML because I want to build a parameterized statement (to guard against SQL Injection) based on a flexible number of parameters which are basically passed in the XML.

The dynamic SQL ends up reading from a table I'll call TableX and I actually discovered an (understandable) quirk with security.

Basically, the connection context is using security for a low-privilaged Windows account ("UserX") and UserX has no permission to the table referenced in the dynamic SQL but because of the dyanmic nature of the query, the stored procedure ends up adopting the security context of UserX. Naturally, this throws a security exception saying UserX has no SELECT permission on TableX.

Now, I can give UserX read permission to the table in question to get things running, but one of the points of using stored procedures is to defer security to the procedure level vs. configuration for tables or columns.

So in striving toward my ideal of security at the procedure level, my question is what is the best way to allow minimum privilege in this case?

I thought about having the internals of the CLR stored procedure run under a different (low-privalaged) security context, but I am wondering if there's an alternate configuration that may be as secure, but simpler.

PS - Please don't let this degenerate into a conversation about OR mappers. I know that happens a lot on these forums.