My only concern would be the ability to hold +/- 0.005
Should be possible with a bushing for the drill bit.good luck holding .ooo5 in any drill press I've used!!
Use two of these pivoting on shafts into the base of the device. Connect the two with a linkage and use a lever, springs, and an over-center mechanism to lock/unlock. You would place the part between the pins, push it up against the stop (you could use a magnet to hold it there or tilt the whole assembly and use gravity). The stop could have a slot to receive the end of the part and a bushing for the drill bit.You might consider a jig that's a variation on that used by woodworkers to drill holes centered on the narrow edge of a door.
For your application a flat piece of steel with two hardened pins sticking up about an inch apart (possibly less) with a 1/8" hole exactly mid way between them. Position this on the drill press table so the central hole is aligned with the 1/8" drill and clamp it in place. Inserting a work piece between the two pins and turning it so it presses against both pins will position the drill at the mid point of the work's width. You might want to add a quick acting clamp to hold the work in place once it is positioned with the aid described below.
A way of setting the end distance would be a round piece of the appropriate diameter on the drill 1/2" above the drill point, held in place with a set screw. A small right angle block could then be used to push against the work end until it contacts this round piece to set the drill position from the end of the work piece.
Positioning accuracy would need to be evaluated by experiment. I haven't built or tried this, just a wild scheme that came to mind when I saw the problem description.
John