Posting in case someone has the same problem.
It turns out it was the carb, which had been getting worse and worse while I waited for parts - I took to Kathmandu Motorcycle Workshop (which is a great shop) with the carb rebuild kit. When they had it out they verified that the seals around the float were leaking (by blowing into the fuel line) and showed me how worn all the o rings were. They put it all back together and now it's starting (and running) much better.
Of course then to celebrate I promptly got a flat tyre
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