I suggest putting a cap on the regular dungeons rather than letting them scale up infinitely. At Lvl 200, the HP of the boss overflows and ends up negative, which is a bit of an anticlimactic finish.
As for how I got that far, I did a confusion bomb build in the cave, which is the only one where this strategy will work infinitely, as none of the mobs have confusion immunity. Asuka and Winry give plenty of bomb generation (Kallen would probably work here too, but I never slotted her in). Chika and Yui together make each bomb give 9 seconds of confusion. My 5th slot, I ended up landing on Megumin to generate some orbs, but you can cycle whoever through that slot, as you will almost certainly net gain bombs over time, which is the only resource that matters if you've got those other 4 girls with the relevant cards. 2 or 3 bombs is enough to make most regular slimes kill themselves. Boss slimes take 4-5.
If you're somehow starved for xp, but have those girls' cards, you can pretty easily get more xp than you'll ever need.