Single Op Through Hole Tapping

Often I get turning jobs which require turning down an OD, center drilling, drilling a hole, tapping it all the way through and then parting the part off. Typically we do this part in two ops. so that both sides get a nice chamfer where the threads start.

Lately I have been considering doing this as 1 op. Our last attempt rendered many parts as unusable because you could not screw a bolt in from the other side (where the part off occured). Applying the chamfer on a drill press, just ruined the threads.

I am looking for ideas on what others do. The material is 1018 steel. The threads are typically 5/16-18, 12mm x 1.5, and so on. The parts are all fairly small (<.200" Dia. Holes) and using a boring bar to put a chamfer on the backside is not an option.