Analysis :: Parallel Period Sliced By Other Dimensions

I have make a calculated member for previous period of an given date range.  The previous period is the same date range from the previous year, and I have managed to achieve that with the calculated member:

Create member currentcube.[Measures].[PrevPeriod] as
(ParallelPeriod( [Start Date].[Cal Hierarchy].[Year], 1, [Start Date].[CAL Hierarchy].CurrentMember), [Measures].[Count]);

This member returns the correct result as long as my query uses the time dimension, which makes sense... but I also need to show results sliced by other dimensions in bar charts that do not display the time dimension.  For example, I have a dimension with only 3 members called [Region].[Area].[AreaName].

The result set for the bar chart needs to look like this:

[AreaName] | [Count] | [PrevPeriod]
East            |    43      |       56
West           |    53      |       95

But the [PrevPeriod] only returns values if I include the time dimension.  I essentially need to sum the results of the time dimension/AreaName/[PrevPeriod] tuple down to just Areaname/[PrevPeriod] for whatever date range may be involved.

I don't know if this is significant to the issue, but the client tool that generates the bar charts builds the query with the date range as a subcube in the FROM statement.  If the [PrevPeriod] is outside of the subcube that is still OK, as long as the time dimension is included in an Axis on the final select statement, so at least I know I am not suffering from the members inside the subcube.  I've also found in SSMS that it makes no difference if I make the query a subcube, or put the date range in a where clause instead;  I still get NULL for [PrevPeriod] without the dates.

I can't imagine that this is an unusual situation, so I hope I've explained it adequately!  What is the recommended technique for summarizing a Parallelperiod by dimensions without displaying the time/dates ?