The new pads were too thick. So the disc was out of alignment with the slot for the disc in between the callipers. If I could of got the calliper closer to the wheel it'd of been fine, but there's no room as the calliper would of just hit the wheel spokes.

Anyway, just bled the brakes (Achievement unlocked; bleed your first brake) and took it up and down the road, it works! It'd still benefit from a new set of (thinner) pads but it works! If I push down it slows me down, if I push down hard the rear slows then locks up, if I release then there's no binding. The rear wheel still doesn't spin freely, but I think my chain and front sprocket have something to do with that (or the rear hub).

I really need some fall back transportation.

i know this is gonna sound silly, but are you sure when you realigned your caliper up with the mounting holes. they were the CORRECT SIDE of the mounting bracket.
it is a tight squeeze putting the caliper back on with new pads but as long as they are identical pads and the pistons are pushed ALL THE WAY IN so they are flush. they shouldnt be sticking out of the bores at all..
i wish i was closer as i would have come and took a look for you. :)

Yeah I thought about that, definitely on the right side of the mounting points, it doesn't bolt on the other way! The pistons were all the way in but it's nothing to do with them as it's the pad leaning against the far side of the calliper that's the problem, the thickness of the pad is a few mm too much for the disc to slot in.

At least it works now.