With the spacers back from the friendly machinist, I was able to centre the swingarm into the frame. With that accomplished, it was time to align the rear wheel -- to centre it in the swingarm.
I am using a drz400 rear brake caliper and bracket, as according to research, it is quite close to being the right size. In my application, however, it needs to be machined down somewhat. So it was back to the machinist with some instructions and some measurements, based on my work with the micrometer and vernier calipers.