Given the options, I'd say maybe a flap like you said maybe have velcro or something on the bottom jaw to hold it in place, but can be taken off if you need to get a drink? And having some vents of some kind to let the air flow still. I'm still working out a solution as well, I was just going to go with a balaclava but if I find something else that would work I'll let you know!
I'd say against the tongue method, only because I'd imagine it would block airflow if it's a thick material.
