I am both a no thumb bowler and a ball driller.
I have also checked this situation with TBA face to face and am up to speed on all these rules.
If you drill a thumb hole, weigh the ball as usual (that is the important issue) to check legality,(i.e. 3oz top 1oz side/finger weight) then that is the time when the thumb must be covered by the palm.
If you want to bowl with no thumb hole, but with a balance hole 180 degrees away then the ball must be reweighed with the centre of grip in the middle of the bridge, using the 1 oz. top/side/finger weight restrictions. This is a lot harder to set up.
As an experiment, I drilled up a ball with three finger holes and no thumb, carefully manipulating the weights to come out close to zero/zero/zero weights.
The centre hole was drilled to the size of my middle finger and both the other holes fitted my ring finger, so I could bowl pin above fingers or pin below fingers with the same ball. Got quite different reactions but it was taxing to remember which way you were bowling, pin above or pin below.
Anyone wanting detailed clarification, can PM me.
I agree with comments above that drilling a thumb hole opens up more layout possibilities.
Sumo