don't worry, such things can happen even on a machine with good alingment
replace the drill with a solid shank, same diameter and length as the drill
use a dial to check that it is paralel to z axis, in xz plane, then in yz plane, thus on 2 generators at 90* phase shift; deviations are allowed, is not critical to hit 0.0000etc, and values can be adjusted by rotating holder, changing tool chuck, changing screws order, using shims, etc
after that, use a coax, to check that tip is as close to spindle center as possible
an y turret will help, otherwise it will be a bit more chalenging
something tells me you have not been throw such a simple yet life saving procedure so far ...
such things are not always related; for example is possible to face and get a clean part, but still have problems with drilling, etc
if you wish, i will go deeper into such things
for specific details, pls show an image of tool + toolholder; is late 4 me, keep in touch
hy jim
it may not be required to spot drill before, i know cases of even longer l/d ratios that worked without internal coolant, for a long series setup, hss drill being changed once at few days ... just be sure that toll is new, in good condition, etc / kindly