Thanks, I thought that the circuit board would probably be the limiting factor. There must be a voltage regulator in there somewhere that reduces the supply to 5V, but it will clearly have it's limits. I would have thought the higher voltage components (e.g. capacitors) would probably be 35V ones, so only moderate overvolting would be possible.
My fully charged NIMH battery seems to be around 29V. This does not seem much of a problem and the bike is very perky at this level for the first few hundred yards, hence my interest. I am considering getting a LIPO or LiFePO4 battery. These are now becoming more reasonably priced and readily available. I am debating whether going for a 9 cell LiFePO4 or 8 cell LIPO, instead of 8/7 would be pushing things a bit too much.