Wow Isaac thanks for taking the time to make this post! That's really awesome stuff and I like how you think
-If the OP says that I'm against the option to allow builders "work" on DE drills as you are clearly showing it does, I'm not sure why I had it say that. I agree with you that they should be an option for builders just as the mines and collectors. As for whether or not the boost that the builder would give the DE drills should be as high as the boost for the mines and collectors, I see strong opinions for both sides.
My personal opinion is that the boost for the DE drills would be smaller than the boost for the mines and collectors because DE has a higher value to players (normally) than either gold or elixir. The cost to gem boost a drill is 3x higher than the gem cost to boost a mine or collector! Therefor I think that the boosts should be something like 1.25x (2.25 with gems) for DE drills and 1.5x (2.5 with gems) for mines/collectors.
As for the way that this feature is unlocked or introduced to the players, my idea there is one of many possible options I can think of. My main reasoning for my idea of unlocking the ability for an additional builder to work every 20 levels is that this would give more purpose to a player's level and make the player more excited to play more and level up and unlock more of the ability!