I took the forks out of the BMX and the MTB to measure them. They both seem to be 1 1/8 inch. The most unusual part is that the simple ball bearing headset on the (cheap, kids) BMX was in much better condition than the semi-integrated one on the (reasonable quality) MTB. I also found that I had more steel than I thought - 3m.
I'm going to order 2 headtubes and BBs from Ceeway, model up the designs in 3D Builder and then create a new thread for each of them, but I'm going to build the off-road one first. I would go to DTek if I could, but it doesn't seem likely to happen any time soon.
Edit - Bits now ordered from Ceeway. Depending on how I get on I might even end up with a round boom (the head tube I've ordered is 600mm long and I only need about 210 for 2 bikes)!