Is it possible to add easing to a looping, time remapped precomp in After Effects?
Add an expression control slider to the layer (Effects>Expression Controls>Slider Control). This will be what we use to control the rotation of the wheel.

now add this expression to the time remap property:

effect("Slider Control")("Slider") % 1


You could also drag the expression pickwhip from the time remap property to the slider property, and then type % 1 after the result.

The % 1 is the modulus operator, it returns the remainder when the first term is divided by the second, in this case the part after the decimal point, so if the slider is at 12.34 it will return 0.34.

Now you can animate the slider using whatever easing you like.