Yes, if your machine has the Neutral Drain mechanism in the transmission, and it sounds like it does by your descritio of the timer pause, then the machine should not be going directly into spin. The agitation cycle is supposed to reset the Neutral drain mechanism each time, so that afte the wash cycle is done and the motor reverses, the spin gear is locked out inside the tranny. During the pause later, the stop pawl in the Neutral drain assy drops down and engages the spin gear.
You have tranny issues, and it is up to you if you want to try rebuilding the Neutral Drain assy or just throw another tranny in there. You should also replace the inexpensive clutch kit while you're in there, as no doubt the extra load of a full tub trying to spin has been detrimental to your old clutch.