You fixed the spring, that means the timer now advances by itself?
What you say has me scratching my head. I can't see exactly what's your problem. You didn't disconnect any wires on the timer other than those of the timer motor?
I thought this machine used a Kingston timer like my 1967 Custom Deluxe (WCDL) but after seeing the picture of the timer motor and reading some documents, I noticed it doesn't (If I'm not mistaken, only the the BOL model, the WCDN and the infinitely variable speed models use a Kingston timer, I thought it was those with the variable water level that used them but I was wrong).
Did you take any pictures of the timer assembly?
You didn't open the timer?
Does the soak cycle work correctly?
Did you try many positions of the "Fabrics" selector? Agitation is fast on "Regular" and slow on "Delicate"?
If you pull on the timer knob or open the lid (I assume the lid switch works) when it fills, it stops all action immediately (it never keeps filling?).
As you probably noticed from the timer chart, with the Fabrics selector on "Regular" during the first spin, the motor should remain on low speed and only the high speed roller should engage on the next timer increment.
On the final spin, it should start with the motor on low, on the second increment the spin roller should engage and in the third increment, the motor should switch to high speed.
If the timer motor advances correctly, the timer should reverse the motor direction between the pause increments, other than that, I don't think there should be any change of action at the middle of a timer increment.