Re: How much thread do you need?
In general, I'd like to see flutes terminate at least a full inch from the crown, because it is CRUCIAL the bore is nice and round there. Flutes tend to (slightly) cause the bore to be out of round -even polygonal in shape.
That said, your flutes are already too close, and adding a brake isn't going to make them closer.
With 7/16" to work with, you can manage 1/4" thread, 3/32" thread relief, and 3/32" of shoulder before the flutes begin. No chance of a crush-washer, but it'll be strong enough to do what it needs to do.
Far from ideal, but oughtta work.