2nd gen not charging right, stator?

Yuasa is probably what came with the bike from Honda. I can't stress enough to make sure your battery and RR are in good shape, it doesn't have to be Yuasa but it has to be in healthy condition. A bad battery can make your RR overwork to try and charge a battery that will never achieve a fully charged status. This in turn will cause the RR to run too hot and destroy itself trying to keep up with a bad battery. This too hot condition will also cause your charging system wires to overheat and destroy the weak links at the connectors.You have already stated that you have had some heat related issues at the starter solenoid. A chain is only as strong as it's weakest link, the same goes for your electrical system.

You may be able to get a good battery at Sears, Walmart etc. Do yourself a favor and fix this stuff. it is cheaper to do it right than it is to get stranded somewhere.

Good luck and hope it all works out!