choose all correct works really well!
I feel like the "choose all correct" questions work really well for teaching all the different variants, which is so good. After experiencing the lessons I've done so far, I think my preference would be to always learn variants organically through the "choose all correct" questions rather than through separate modules for different regions, levels of formality, etc. Especially as I live on the north/south dividing line and people here seem to mix it up a good bit.
I agree multiple choice questions are far nicer for learning the different variants, it would also be nice imo there was some way of distinguishing which phrase was which variant in the lessons themselves. Trying to talk to my Gran in Welsh has led to me slipping into north Walian a few times without realising (which is fine if you're on the dividing line, but inside the M4 corridor, less so :P)