Update:
I hit up Mack from THA, and I ordered a custom 4.5 inch Inception Chamber with very narrow tunnels and an internal water tower. I hope this works.
My time has come. You can def put them in a normal formicarium as long as the tunnels are narrow enough. Feed them dead insects, springtails, symphylans, and maggots, as well as a bit of sugar water soaked into paper. Keep them relatively moist. Hypoponera are surprisingly active for a cryptic ant and can forage in open areas. I've noticed they don't tunnel all that much(well they tunnel a lot but don't use said tunnels except to move around to new foraging areas) and nests are fairly localized within one small spot, so no need for intricate nest design.
The little guys are actually doing surprisingly well in the dirtbox setup I placed them in. I opened the bottom hatch to hydrate the nest assuming they wouldn't burrow that far but lo and behold, an ergatoid and two workers peeped outside. I was not a proponent of escape heists, so I quickly plugged it back up.
I wonder if I can feed them mealworms or red runner bits. They actually like earwigs for some reason as well. I don't plan on getting them any sugar until I move them into the Inception Chamber I ordered, since dirt + sugar residue doesn't sound like a great combination. However, I'll feed them daily, it seems they like springtails and earwigs, so I'll do a little bit of daily experimenting and see where it takes me.