I think I've reached the end of the line on this one. I've had discussions with Insurance Agents to see whether anyone would entertain the idea of one policy covering a group of named people, playing individually, or as named bands. It seems that the insurers would be unlikely to agree to that, except as an expensive bespoke policy, because that's not the way it works.
I still feel that many of the 1013 visitors to this thread, and the insurers, would have benefited from such an idea, but it looks like it's not to be. The best option at the moment for anyone who wants PL cover only seems to be to insure each named band they are involved with, or the individual, under separate policies.
Horses/water.