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Some incredible hacking skills, likely beyond me, though I could consider approaching some of the workshops in the uni I work at. Not super in to the idea of re cold setting my frame
I think I see how your second proposed solution works in terms of aligning the caliper to the wheel. Once set in position am I right in saying that you would need to take out the skewer completely to get the wheel out (unless you make it open ended as suggested).
(Random idea...)
You could make this (green part) as a 1-2mm thick steel plate and either clamp it on the outside of the dropout with the 2 brake bolts and the left wheel fastener.
or run it on the inside of the dropout (so the frame is slightly widened to 136-137mm)
It will keep the brake aligned with the wheel.
Extra bonus finesse would be to have the 10mm hole for the wheel axle be open ended