"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.