[Dan Heck]

I think you've identified the problem:

".....FYI, the motor is a Lucas (oh no!)...."

Nevertheless, I'm sure there are many here who can offer more informed advice than I can, but if yours is an old junkyard Lucas wiper unit like mine [$15; whatta deal!], perhaps the grease in the motor's gearbox or the tube may just be dried out and stiff so that it loads the motor and blows the fuse. Your speculation that a bind in the cable drive or the 2 gearboxes on the wiper shafts might be loading the motor sounds reasonable as well. I took mine all apart and cleaned & greased it up well when I salvaged it-the construction and assembly of the mechanism is simple and straightforward, so I wouldn't hesitate to dig into it & check things out.

Dan