It sounds like you're right on track to getting this beauty running automatically again. The water valve is pretty straightforward, looks like the hosing is going well and that leaves the timer...
I would start by removing it from the machine, taking off the timer motor and checking to see if that runs when it's off the timer. If so, you're good to go there. Replacements can be found, but it can be challenging. It could be that the escapement just needs a bit of cleaning and light lubrication.
The replacement gasket (spud) looks like a brilliant solution!