I did find a way around this issue. I was able to add a unique tag to each cell component (e.g. id=<table>.<column>.<uniqueRowIdentifier>). Next I wrestled with getting the CheckPoint Wizard and the Name Mapping to use id as their primary selection criteria. (I never did find it. I noticed that the QuickCheckPoint feature does this, so I am just going to use this from now on.). And now my current issue is getting TestComplete to hover over a specific cell in the table and select a button that only becomes visible during a hover. All these things have probably already been solved by somebody else somewhere and it would save myself, and other newbies, enormous numbers of hours and frustration if there was a central repository of Angular/PrimeNg specific information like this, or a specific group of "power users" that we could ask. I already have a series of pretty extensive Confluence pages with what I've learned so far to help other users in my organization.
Thanks for all the suggestions y'all have given so far, though!