Bike.1 was the one that got a motor transplant from China. The motor worked, and the associated controller electronics, but when I gave it full throttle, the battery kept switching itself off.
So I went back to the Chinese supplier to get a battery. The first one I ordered simply didn't arrive, I don't know why. The second one, they were unable to send. I think it has to do with regulations covering Lipo batteries on passenger aircraft. Anyway, they gave me a refund for both, and apologised for wasting my time. Fortunately, bike.2 was working fine all this time, so I wasn't seriously inconvenienced.
That was what set me off on a battery hunt that eventually led me to Hobbyking; the Hobbyking batteries I bought were 20C, which meant that they would be able to supply 100 amps, and all I wanted was 20 at most. I bought four, because I didn't want to buy a full set until I knew that my plan would work - after all, what I'm doing here is taking stuff intended for model aircraft and suchlike, and using it for my bike. It did work, but buying the other eight batteries turned into a nightmare. They sent the wrong order, I sent it back, they're out of stock, and that saga continues.
But yesterday I had a thought. Suppose I run two of my old batteries in parallel; then each of them is only supplying 10 amps, which it's happy with, but the motor gets 20. So today, I wired up a parallel driver cable; two male kettle plugs connected to a female, with a 25 amp fuse wired in for extra safety.
And today was testing day. First I tested bike.2, with its new controller. That worked fine, so I put it in the car for use in the near future. Then I tested bike.1, with the new motor from China, and the two old batteries in parallel. I got it out into the road, and gave it full throttle. Before, when I did that, the battery cut out. But now, the two batteries, working in parallel, were happy with the current load, and it all worked fine!
So now Hobbyking have put my order back in their pipeline, and as soon as suitable batteries arrive in the UK, they'll deliver.