Yesterday's photo's are of the cylinder and engine that came with the bike. Not very good news obviously. I have two very crappy spare engine, but I manged to combine the cylinder of one of those with the piston of the other one and put those back on the first one. Lo and behold: It works AND the smoke is gone!
And my girlfriend's been riding it. She liked it a bit too much, I'll have to live with sharing this bike.