I ended up using a mixture of these ideas. @Leith, when I ran your code, VBA did not recognize the "Excel.Button" dimension and started deleting sheets left and right. (Amen for backup copies, right?) So I defined it as a shape, the way @Gatti did, and it recognized it after that. I just ran a test where I added a sheet and put a form button on it, but didn't name it the same way, and the code deleted that sheet and left the rest. Perfect! Thank you all!
I have a ton of things going on already in the BeforeClose event, but here's the snippet of code I ended up using for this:
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