There is another possibility that has occurred to me. When you
rebuilt the coil what did you use for a condenser. My only
experience using a capacitor would produce a spark when tested
but the motor wouldn’t run. Turned out the one I used wasn’t fast
enough. (This was determined by another member – I have
little understand of this stuff.) If you in fact used a condenser
you may not have it wired correctly. As you are getting a spark, to
test if it is a condenser issue ground one anywhere on the motor.
Run the wire to the coil connection in the timer and and add it to
see if it will start.
Tubs.
A "Boathouse Repair" is one thats done without having tools or the skills to do it properly.