This my third go at getting somewhere with my ailing boiler.
The problem now appears to be that the thermocouple is failing at high
temperatures.

If your boiler is old enough to take a thermocouple, you might want to
consider replacing it. A modern boiler would have 90%+ efficiency, instead
of the 50-65% you are likely to be getting now. It may be worth making a
judgement on whether or not a replacement would make financial sense,
particularly if the old boiler is starting to keel over. There's a lot of
gas to be saved.

Christian.