We sorted this out this morning - turns out it was the earth strap, although a slightly unusual presentation of the problem.
Obviously I cleaned all that stuff up when the engine was out, but measuring the voltage while running showed 14.2 at the junction box but only 13.3 at the battery. This left the battery only 40% charged (and unfortunately 40% health) hence the lazy starting. When I investigated further, I discovered a layer of grey aluminium oxide dust between the earth strap and the mounting block on the body. I think the reason it got worse to start when hot was that all this area gets hot as well and so everything expanded a bit, including the aluminium oxide dust, thus reducing the available voltage even more.
Cleaning up the terminals with some scotchbrite got rid of the dust, and with a replacement battery fitted it jumps to life as it should
I gave everything a coat of waxoyl to hopefully prevent corrosion getting back in again.