The first GE combo did spin between water changes if literature is to be believed. That was the machine with the transmission and was redesigned. Spinning was a royal pain for most combos because of the lack of a suspension system and the lack of effectiveness of the low-speed spins. If the load did not balance, you could lose time meant for spinning for tumbling to redistribute and, since timers were not held to balance the load, it could be time basically wasted and only extended an already long wash and dry program by building spin segments into the program. I think that the sequence of the spins varied greatly from none at all like the gas combo sold under several names or until the end like the GE or some like Easy, Norge that spun once or twice during the rinsing sequence, some like the Bendix sequence with one spray rinse and two deep rinses followed by spins and the WP-made machines with a spin after each drain. WP-made combos kept that sequence after they redesigned the machine to be able to provide a high speed final spin and slower speed intermediate spins after earlier water changes.
Now the GE combo's cycle, to answer your specific question was, as best I remember from the one I used: wash, drain, rinse, drain, rinse, drain, rinse, drain stop. You have to remember that the GE combo reverses to drain, much like their dishwasher motors. The combo does not spin until after the last rinse. The spin portion of the cycle has three phases of tumbling and spinning followed by a stop. After the final stop, the drum begins to tumble in the drain direction so that condenser water can drain during dry and the heat comes on. How much heat depends on whether regular or delicate dry is selected. If regular dry is selected, the heat cycles on during the spin sequences. I think that is all I remember and what is correct.