My colleague @Thomas Riedl very kindly printed a new Wade's Extruder main part for me, being careful to get the support off nicely. It required a bit of drilling, sanding, and dremelling to get all the parts in, but at least it looks solid.
Alas, the weird version of Wade's I had was not only narrower in the hotend mount, but also taller, so the large gear doesn't fit, it hits the X carriage in a place where I can't just cut a hole.
Fortunately, I had also ordered a Greg's Hinged Extruder, a molded rather than printed version, just in case Thomas ran into problems. It has a strange rubbery top to it, which I a bit later found out was is because they have pre-inserted and closed off the two hex nuts:
So I remount the motor on that, only to find that the gears are not compatible and I could not get the small gear off the motor rod. I suppose I could get a new motor and finally have nothing left of the original extruder. But the old large gear does work, so I can use that instead! After mounting that and the idler, getting the hotend fixed was difficult. Due to extra lee-way, the left-hand screw would actually move the hotend down on its side when far enough in, making the hotend slant:
I'm pretty sure that's a bad idea. But that's not all, once I got everything together, I found that the extruder mount was right-handed instead of left-handed. See how it sits over the edge of the X-carriage with space left on the left:
After disassembling it, I found the mounting screw had actually dug into the hotend:
My best option now seems to be to have Thomas print a new large gear - looks like I need a 37 tooth 5mm pitch gear, though it's possible a 39 tooth one would work, which is nice because that's the normal one with Wade's.