Note there is a simple way to get clothes drier in washers which was suggested in the owners manual of my current top load washer, in particular towels and the like. Give the load an extra spin (the washer has a spin only cycle). This does extract some more water and uses very little energy once the washer is up to speed.
A few years ago, I actually did a relatively scientific analysis of this. Probably have a file on my computer somewhere, or maybe not as the results were not impressive, at least with my washer.
I took the load of clothes out after the normal washer/spin cycle, and weighed them on the digital kitchen scale. Then did another spin and another, weighing each time. And again when they were dried, so I knew how much water weight they retained after the first spin.
The numbers were measurable, but too small to justify even fussing with the playing with the dials, and coming back again after that spin cycle was over. I think maybe the extra spin removed a few percent extra water, the next spin an even smaller delta (as expected).
You might get different results on a different washer, but I imagine the designers already had a pretty good idea of where the point of diminishing returns were, and stopped the timer there.
But if you really want to know, that process should give you a pretty good idea. And yes, your spouse will be quite entertained by this
But if you do measure a difference, it should save some energy - you are correct that the spin cycle should take less energy than the drying.
-ERD50