Okay, so I tried to replicate the issues I saw last week I couldn't, so I'll mark this issue resolved. I will note that there appears to have been 2 PowerApps releases since I first noticed my problem:
3.18073.33 - When I imported App A into my test environment on 8/13
3.18072.29 - When I imported App B into my test environment on 8/14
3.18075.22 - When I saved both App A and B for the first time
3.18081.19 - The version I saved and published both apps on Friday 8/17
So maybe MS tweaked whatever issue I was having last week.
-Jamie