Now that you've got the source terminal grounded the gate would be fine with 5 or so volts.

I'm not sure why you'd want to use 5V when a higher gate voltage is easily available.
Since the FET conducts appreciable current its resistance should be kept low.

The only reason really for reducing gate voltage is to speed up turn on / turn off and reducing switching losses but even 500 Hz isn't fast in the least and right now he's manually switching it.

 

I've actuated the gate with 300hz cycles and it vibrates like crazy! It sounds hellacious!

Would it not oscillate like this if hydraulic pressure were forced against it?

 

This now depends entirely on the exact mechanics of the solenoid.

High inductance may be preventing the current from dropping to zero so the solenoid would not move as far as it should.

Even if current drops to zero the solenoid has some mass which will delay its movement so again it might not be moving the full length.

Having more force on the solenoid will damp out crazy oscillations yes but it might just mean it barely moves.

You can make the current drop faster if you put the diode across both the 4ohm resistor and coil. When the FET turns off all the current goes through the diode and that diode voltage drop is what makes the current decay. By keeping the resistor in the loop you add the I*R voltage to help with the decay.

 

You can also speed things up by eliminating the diode entirely and putting in a zener diode from drain to ground.