I can very clearly understand the frustration from frequent use of non-standard sizes. I imagine that will always be a can of worms.
Have you experimented with using a safelight filter for your enlarger, and an external border-exposure-light?
Possibly the neatest way I've seen someone do aligned black borders on random sized prints was to do their print exposure normally, then put a safe light filter in so they could keep the projected image visible on the print. From there they would put a solid mask on the print while leaving one edge uncovered, use a bright lamp next to the enlarger to expose the edge, then repeat for the other edges. - Sharp, well aligned borders with a perfect match to the print's black tones.
This thread reminds me that I need to sort out a reliable way to do this with my contact prints. I had been planning to make mask frames for white borders, but after experimenting with my prints without a mask just for the general trial exposures, I've decided that I kind of like the black edge instead... but I haven't yet settled on a plan that sounds quick and easy to keep alignment on everything for the print exposure [with the glass and negative press] and the border exposure. Building a two stage vacuum table may solve some of my problems however...