So to me it looks like the EP2000 is faulty (and may always have been) as
'off' doesn't seem to do anything, and that now that wall stat has gone
short.

Does this sound sensible? I don't really want to replace the EP2000 if
the stat is faulty, and vice-versa. Also, I'm not sure if the newer
EP2000 is compatible with the backplate of my older one (any ideas?).

It could be the three port valve that is sticking...
If you remove the timer from its back plate, does the pump still run?

Sparks...