Static damage is correct.

There would be two values: average dice (rounded down) for regular hits and maximum damage for critical hits. I know, more math, but there's not much work to it at all, I think. Besides, you'd only be doing the math once as opposed to math every time you roll damage.

I'm on the fence whether or not extra damage dice (sneak attack, magic weapon critical, etc.) should also be static or random.

There would be two values: average dice (rounded down) for regular hits and maximum damage for critical hits. I know, more math, but there's not much work to it at all, I think. Besides, you'd only be doing the math once as opposed to math every time you roll damage.

I'm on the fence whether or not extra damage dice (sneak attack, magic weapon critical, etc.) should also be static or random.