I've had multiple calls with ESRI tech support and we haven't made much progress. They thought it was a cross network drive issue, but the problem persists when exporting the project to a pagx file on my local C: drive, and sourcing the table frames from an Excel sheet in the same directory. I DID discover something very interesting today.
If the table frames project is the first project I try to open after starting Pro, then Pro crashes, or the layout opens and the table frames are unsourced. The source in the properties pane is correct, but the tables have exclamation points next to them and the table frames just say "table frame." If I open another project first and then navigate to the table frames project without closing Pro, everything is fine and the table frames are sourced. I have recreated this behavior multiple times and it works every time. This smells like a bug.