The trouble with solenoids isn't just the transition force, but being able to remain engaged so the case doesn't pop into neutral. It would either have to have a holding coil, as the heavy switching coil would draw a lot of power, or it would have to over-center a spring that would keep pressure on the lever.
The case doesn't just shift when you flip the switch, but the vac motor holds pressure so that when the splines line up for the shift it will pop in, then it keeps the lever solidly engaged. The only "electric" option I've really come up with would be to use one of the vacuum electric "emissions" solenoids and actuate that with a switch.