Don't think I will help OP at this point, but for anyone else reading I found a quick fix.
I have a drill chuck that is about 5" from end to end not including the taper. Add 3" of drill bit and that is a long distance. It also seems to be slightly off center from the time I got it new. But perfectly centering anything over a distance of around 8" is difficult.
I also bought a pen mandrel that came with a morse taper and collet that was built to hold the (I think 17mm) mandrel. Its not made for it, but that collet holds a 1/4" drill bit perfectly and is what I use to drill my inserts. It only sticks out about 1" from the tailstock plus however long you want your bit to stick out from there.
The only downside is the size of the collet pretty much only allows you to use it for that specific purpose, but I can still use my drill chuck if I don't need as strict of tolerances.