I seem to keep running into dead ends with these common cathode LED displays. Anyone have any other suggestions?

Yes, use common anode displays.

I know this may be an expensive lesson, but it is important to have the design before you buy the parts.

Anyhow, of course, you can use common cathode, it is just more of a headache.

If it has to be done, then use an Allegro high side driver to multiplex the anodes and an Allegro low side driver for the cathodes, decode the segments in code and off you go.

Erik