LDO regulator (LD39300) output capacitor ESR not so small
You are correct in assuming that going outside the stability regions is a 'bad idea'.

It's difficult to predict exactly what will happen if you operate outside the stability region of a fixed-feedback regulator like the one you're describing. The regulator may start oscillating immediately, or appear fine but start oscillating if there's a sudden input or output change.

Blindly adding capacitance here will likely make things worse. Don't add the monster cap, or if you need super smooth output, change to a different LDO.