I think the temptation may be to take too much wood off, because visually, the proportions of the Telebass / early P headstock come partly from the wider 40mm nut... so I'd maybe just take the lower hump down a bit, but what do I know? (rhetorical).
(Yeah, it sounds happy enough. Reminds me of Haircut 100)
(I can't actually remember one Prefab Sprout tune, from all their 10-odd albums and Mercury prizes)
Ah, so there's not much threaded end left on the rod, I suppose... Actually, from that pic -- the strings were still on... is there a bit of rod sticking out now the strings are off?
Seriously though, is there a cheap way to remove a 'polo mint' of the wood around the snapped rod?
glass paper stuck onto the end of a bit of dowel with the center hollowed out... ? spin that up in a drill ...? you'd only have to go deep enough to get a slim nut and washer on the end... I assume there would be plenty of depth of wood there...
Might need to carefully file the snapped end of the rod to accept a nut...
@Reggaebass -- would that be likely to work at all?