This doesn't make sense to me. Shouldn't the rim be centered on the over-locknut width? If so, flipping the wheel shouldn't change the rim-stay distances.

When I run the string exactly as you show in the previous post, the string-seat tube measurement is identical on both sides. However, if I tie the string off at the brake bridge, it's off by almost 2mm. So it looks like I have a sloppy frame.

I'll talk with the local shop and see what they'd charge me to scope it out on the table and see if adjustments can be made. This isn't a bike I want to sink a bunch of money into. If that course is cost-prohibitive, I'll fudge it the best I can.