Belching oil from top of engine (breather) and lost power

It's certainly an interesting case. I've had time to clean everything up a bit now. I can see the bores aren't really perfect - that one (with the obviously damaged piston) has a little notch in it near the top. It's not deep though. 
More interestingly, I've found lots of little bits of piston ring embedded in the cylinder head! Stuck in there like little daggers... Those are the larger bits anyway. There are also what look like carbon deposits but are more like burning steel debris. Anyway, luckily I've got another head.

Tbh I haven't decided what to do with it yet, and haven't even ordered any parts. I think I'll just sit on it for a few days until the answer's obvious.

IMO you can't go halfway and expect to fix this.  If you decide to repair it, you'll have to go all in.   As pointed out already, leaving any debris inside could lead to big problems.
 

Yes, I agree. At the moment it seems to be pointing that way.

It's been a very interesting journey with this project bike. It was fulfilling setting it all up. It was also a fun time riding it, although perhaps not the best thing for my 4-cylinder riding style so not exactly a 10 out of 10 riding experience. It was just a reliable, generic, pleasant and nice-sounding old Japanese bike with character. As it's a low-value bike which will never be a sought-after classic, and I could afford to get a new interesting project (I'm always thinking about old Urals, for some reason, but also other Kawasakis), and it would cost money to do this properly (there's no point splitting the cases unless I'm gonna renew all the bearings and check the state of wear of major components and replace as necessary), I'm just gonna sit on the fence for a bit. It would be a pain in the neck pulling apart this engine. I've also thought about parting it out. I live in the UK, and motorcyclists here are a bit all-or-nothing. There will be no demand for this bike as it is, or its good parts at all, for many years, until one day they might suddenly decide they're desirable. When that happens, the parts will suddenly be valuable as they're very scarce here. Until that time, I don't want to hoard junk as I have just an ordinary house and garage. So if I sell anything (whole or in parts) now, then I'll be basically giving it away. Then again, a project bike is like your kid. You don't just give up on a kid that's got problems. People give up on people all the time - that's just human nature. But not me. I'm going to have to take time out and have a good think.

you can always just set it aside while you concentrate on other motorcycles, since you won't be tying up a large investment.  (Assuming the space is available)  Then at some time in the future it might become interesting again.  Who knows, you might stumble on a donor to make 1 out of 2 with very little effort.   

Scotty