Right, so the starter turns (most of the time). I'll swap it out with the brand new one that's coming tomorrow. The trouble is, the fuel pump's either stuck, clogged or shot.
Unhooked the fuel pipe from the (mechanical) pump and cranked it over, no suction whatsoever. It fired once or twice when we blew fuel through into the carbs, so I'm pretty confident it'll run when I replace the pump.