We are instructed to not wear a watch on the field. I can't imagine there being an exception for wearing it on my mask instead of my wrist...
We have one park here that has scoreboards with game timers. When I've umpired on those fields, we inform the scorekeeper when to start the timer, and after that, it is up there for all to see. It works well, and has not been a problem. Sure, it MAY from time to time have an extra inning played over what would happen with a shaved timer in the pocket. Big deal. If the game is going to have an official timer, what is the problem with making it visible for all to see? Seems to work for any other timed sport.
I don't understand the objection to a timer on the backstop. Although I've never done that, it does not seem to be a big appearance issue (it's on the fence fer cryin' out loud - along with bat bags, helmet bags, lineup boards, and water bottles...) The Seattle approach to this seem highly anal, to me.
As to the math... if you want to really be precise, you need to include in your calulations the curvature of the ball and the thickness of the timer to determine how close the ball can be to the timer before it actually hits it. Talking about anal....