So, if a guy is restricted to submerged snares in an open water situation, what is the best way to go about setting them? Just set them as you would a bodygrip? Dive stick over a channel with a snare centered under it. Snare set at the bottom of a run. In front of a castor mound with a dive stick. I know its a horrible situation but its what I am dealing with.

Yes
Set runs just like you would with a body grip.

I never set a underwater snare with lure.
Somebody on here probably does.

Does the snare have to be completely submerged or halfway in?

Fully submerged. Partially submerged I am use to dealing with.

I’ve only done partially submerged snares with beaver. Considering your restrictions, have you tried cage trapping them? Kirk DeKalb has one, I believe Comstock has one and Ztrap does too.