I'm surprised they're not through holes-- since you're not going to use them in the rain you can probably do through holes (all the way to the spindle space) and then use threadlock to seal it. I can't imagine it's thick enough to get all that many threads, and with a blind hole you can't thread to the bottom, so it could be hard to get the screws to stay tight.

If you're doing blind holes and have a friend with a milling machine it's pretty straightforward to get precise depths-- you move the table up rather than the head down, and most have pretty precise control over the table motion.