Should I just spring for a new MC and try that before replacing all calipers?

Yes


Is there someplace here that explains a bit the process of "bench" bleeding?

MC should come with fittings and little tubes, attach the reservoir, hook up the tubing and return it to the reservoir, fill the reservoir and start pumping. I typically hold the MC and push on the rod. Do this while watching the fluid returning to the reservoir and when it has a good flow you should be good to go. Use caution and don't spill any on the paint work. It will remove paint.

Replace the reservoir and the rubber bits used for the seal and the little pushbutton thing on top if it has one.

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Jim