So I got a bit carried away and did the other 3 Materia Caves in the following order:
Mimic: fairly straightforward, my standard setup was enough to grind through to victory.
6 Heroes: first set wasn't too bad, but I was caught by surprise by the second set and misplayed horribly. For example, not realizing that Green Hero's Dragonsong was applying mass Regen... came better prepared to set up for the second half of the fight and it wasn't too bad.
Omega and Shinryu: Somehow won on first attempt. I knew about Omega's Stop vulnerability, and managed to keep it out of the fight for the most part. Encircle was nasty, but hit support-tank Cloud so it wasn't a huge deal. However, something weird happened at the end: Shinryu used Zombie Breath and Cloud was subsequently KO'ed, and I got the pop-up when I revived him with Life2. In the same turn, without zombie-Cloud ever getting a full ATB bar, I finished off Shinryu. When Shinryu used its final attack counter Almagest, Cloud took no damage while the other two party members died (Tifa lived with Grit), and the game recorded that as a victory. Cloud got EXP and AP as well.
Great Gospel was key in all of these fights, I made sure to start with access to it, and usually managed to fire off another during the encounter. I had somehow forgotten about Comet during the Quadrangea fight and swapped to it afterward as my primary damage source, along with Tifa's Deathblow+Added Cut and limits chipping in (I couldn't use the Curse Ring/Powersoul combo though, I found it too fragile).
Fun fights and a good level of challenge. I had to use a handful of Megalixirs which likely could've been avoided with cleaner play or higher levels and better preparation, and while the bosses were very threatening it all felt mostly fair, with counter-play available.