So I got a chance yesterday to compare my new digital angle gauge to my phone...
Not only was the new gauge a lot easier to use, but it appears to be more accurate. When I zeroed both on the table top of my saw, then measured the blade (set to what I thought was 90 degrees), the digital gauge showed 87.6 while my phone showed 89.9. I checked a few time just to be sure, and also checked my miter saw to verify. The results repeated themselves.
So after re-setting the 0 and 45 stops on my table saw based on the gauge's reading, I was surprised to find that it seemed to cut better and quieter.
I still have to double check a cut piece with a square to see if it's actually cutting at 90 degrees though.