After some more experimenting, I think the issue relates to the MiSTer.ini file.
I went through a fresh install/format of my SD card and did the entire setup up until adding the MiSTer.ini (for my 15kHz arcade CRT). Connected via HDMI, I was able to load SSF2T perfectly fine 10 times in a row without any problems.
After adding the 15kHz-YOKO MiSTer.ini file, the glitches/flickering came back for SSF2T.
I tried this experiment twice as follows:
1) After adding the INI file, I powered the MisterCade up in my arcade cabinet. Upon the first load of SSF2T, the glitchy/flickering was present.
2) After adding the INI file, I set the bootcore to lastcore, and connected it to my HDMI display and used the Nano DE-10 power supply. First load of SSF2T was good. Powered it off and back on. Second load of SSF2T had the gliches/flickering.
Since this occurs regardless of what display or power supply I'm using, I can only hypothesize that it has to do with the INI file somehow.