When I first used lathe for drilling, I was indignant that it was not nearly as precise as my hand drill!
When hand drilling, I first drilled a pilot hole for the chamber with a forstner bit, staying a little short of the intended depth, then followed with a round-nose twist bit,
still short of the intended depth. Next was the precision job - draft hole. I fixed the vise on the cross bar of a stool and let the stool lie on the floor so that I could stare
down at the workpiece. Chuck the block in a manner such that the planned draft hole is at right angle to the floor. With one leg on the stool to stabilize it, I drove the hand drill
down toward the
planned bottom of chamber. The crucial tip here is to concentrate 70% of your attention on left-right centering in a manner similar to training a pistol, 20% on front-back orientation, 9% on
not over reaching your planned depth, and only 1% on flexing your triceps. The 1% part aims to force you to go very slow and keep to the center. After the draft is finished, re-drill the chamber to the point where the draft hole precisely touches the bottom. The previous chamber drilling was made shallower than the planned depth because you can always drive down a bit more to meet the target, but if the draft hole enters several mm above the bottom, it not only affects smoking but also makes shaping of the bowl chin pretty risky.