The mills quill lock mechanism is rather spongy, there's quite a movement between free and locked. Move the quill up and down while tightening the lock and you'll see what I mean.

If you changed the lock mechanism to a straight push and lost the sponginess then the short power throw on the solenoid would not limit your lever length.

Presume you are aware that solenoids come with a duty cycle? If you turn a 20% duty cycle solenoid on for 10 seconds you have to leave it off for 50. You can get latching solenoids but they require pulses in both directions and the electronics becomes awkward.