Hey there machinists. I've got a shop available with some lathes, drill presses, and a milling machine and I want to drill a hole with a milling bit in round Delrin stock. I need the depth of the cut to be accurate to a few thousandths of an inch (looking for 0.215" and 0.160" holes with 3/8" diameter). I've already faced off both ends of the two pieces I want to drill into so that the faces are flat and square to length.

So my question is, what's the best way to do it?

The lathe seems like a great option because I get the hole centered for free. But only one of the lathes has a tail stock with length markings and it's not very precise and can't be zeroed. One of the drill presses has a depth stop but again it's not very precise. The milling machine seems to be the tool to use, then, but so far I haven't found much information about getting a good zero and accurate depth (I have very little experience with the mill unfortunately).

If I'm able to track down our resident machinist I'll ask for his advice but I was wondering if anyone here had any pointers.