Sounds about right. There is no other way I don't think.

Currently if I'm in a multi-part performance and make modifications to a specific part and rename the part then save, I don't see that renamed part available for other performances. I only see the new renamed parts when I save them as a single-part performance

The Part you created is available for other Performances... So there is no need to save it separately you can always have access to it by searching for the Performance you created for, then setting the SOURCE PART # when executing the Part Merge.

Say you create an additional Part or you modify and rename a Part, when you STORE this as a new Performance your newly modified Part is stored as a member of that Performance. You can now access that in any other Performance slot using the Performance Merge function.

Say your modified Part was Part #3 (you renamed the Part "StephansPad") of a Performance called "Set Opener".
When you are looking for it, to add to yet another Performance, you can search for it by the name of the Performance you created for.... Set search for "Set Opener"
Set the SOURCE for the Merge to Part = 3

This will merge the "StephansPad" Part to the new Performance

When you press the "+" to ADD a new Part it takes you to [CATEGORY SEARCH], set the SOURCE Part setting on the top line to "Part 3", find your Performance "Set Opener.
You must have version 1.10.x to have this Merge Part feature.