To add to what Les says, alignment on a wood lathe is not quite what it is on a metal lathe.
I find the only time it is frantically important is when end drilling, to be sure I get that right, I create a small recess in the centre of the timber with the tip of my skew so that the drill bit centers correctly.
Try this;
Deliberately offset your headstock by a few degrees and put a spindle between it and the tailstock livecentre, align your toolrest to the slightly skewed angle, you'll still be able to turn a parallel cylinder.