I decided to run a simple test case...just two shapes. Unfortunately, it was late, so testing is incomplete. Using custom shape name vs sheet.ID was fine and then broke, sometime after grouping. My procedure was as follows:
1) when doing the grouping, I made 1st shape the group. See Ribbon>Developer>shape design section>Shape Name. This brinfgs up a form that shows ID, present name, e.g., Sheet.1, and other info. This will be used this to change shape name.
2) in shape 2's shapesheet, created a single Shapedata entry, for convenient reference and value changes. Named the data entry "MyVal".
Then, added
DOCMD(1312) in the Event double click cell
3) back to shape 1's shapesheet, I set this formula in the height cell:
=Sheet.2!Prop.MyVal4) no grouping at this point.
This works as expected. double click shape 2, brings up Shapedata entry form. Setting different values causes shape 1's height to change. Next step, change shape w2's name, something simple, like Sqr2. All still works. Open sheet.1 shapesheet, and in the height cell the formula now shows
=Sqr2!Prop.MyVal. Visio updated the formula to reflect name change. (Note, subsequent, additional name changes will not get pushed into this formula and are ignored.).
At this point, converted sheet.1 to group and added sheet.2 to the group. The sheet.2 is still named Sqr2 as no other renaming was performed. Changing Sqr2 prop data still works. That's as far as I've progressed.
Edit:
Things left to explore...
1) more complex shape names
2) impact, if any, doing a more traditional grouping approach.
My suspicions are...
1) The subshapes may have been renamed multiple times. If so, that's a problem. See
http://visguy.com/vgforum/index.php?topic=8417.msg36441#msg364412) Grouping might be a factor, but I wouldn't think so. Unless M$ introduced a bug/feature that doesn't accept custom shape names.