I do use blocks too but using them means I also throw the center of the self centering vise out of wack. Blocks do seem to be the easiest solution but still not a "good" solution.
its dangerous, but you can drill as much as you can, shut the machine off and raise your bed with the bit inside your piece, then turn on the machine and drill some more. it would be safest if your piece was clamped.
Also, if you purchase a drill chuck with the same taper as your lathe, you can do your drilling on the lathe. Thats how many of the plug builders do their through drilling.