If the motor is running in the correct direction during the spin cycle then the transmission/gear box is bad.
I would guess being you have already replaced the timer then the motor is running in the correct direction for the spin cycle.
I have only seen a few direct drive washers do this over the years. They end up agitating well the basket spins and it wraps the cloths around the agitator.
Gearbox (Gearbox, Transmission, Clutch) Part #3360629