Has anyone successfully repaired one using anything other than the diaphram supplied in the kit? I’m thinking of a piece of innertube cut to fit, not sure how it’ll last being in contact with brake fluid.

Don’t do it. There is some things you can Borge, brakes are not one of them. Avid do a leaver service kit.
I just replaced the piston seals and had the cap off. The screws have to be done up very tight on mine to stop leaks.