"George" (clip) I had the idea to turn a piece round, then, using the index,
rest and boring guide, bore through-and-through, assuring alignment of the
spokes for rim and hub. Didn't work well at all, as the bit followed the
grain, resulting in a visible misalignment. (clip)
^^^^^^^^^^^^^^^^^
If I understand you right, you are trying to make disk wheels, with round
bored holes through the web, to create "spokes." I can picture these,
perhaps painted in a bright red, with fancy pin-striping, kind of like a
circus wagon. Very attractive.

The first suggestion I will make is to find some wood that has hardly any
grain structure (like pine) so the drill does not have a soft off-center
path to follow. I would use a close-fitting drill guide attached to the
toolpost, to minimize drift. And, I would use a Forstner bit--they have
very little tendency to wander.

Another possibility, if your lathe is big enough, is to make an off-center
jam chuck, so you can TURN the holes. By rotating each wheel to six
different positions in the chuck, you will create the spoke pattern you are
looking for. This also has the advantage that the holes do not have to be
straight-sided, so the wheels will look lighter, and more "sophisticated."

If nothing else works, you could just give in to the problem, and make the
wheels out-of-round, like a cartoon coach. And never reveal that it was a
"cop-out." It was a humorous innovation.