I worked on the Special first cleaning out all the dirt, grass and mud wasp nests and with some attention to the electrics and carbie it sprang into life. The Export was today's job and I have just had it running for a good half an hour as well.
I figure most of these mowers are laid up for simple reasons such as points etc causing hard to start problems and then parked in the corner for years on end.
Looks like somebody modified the pulley for the model 5. Also the department store model looks like somebody tried to repaint it. It appears that you are having fun though. Good work.