Your diode parallelled to the mosfet must be paralleled to the MOTOR ... that will GREATLY limit the spikes ( 1N400x seems a bit Weak for this kind of motor ... try better 1N540x or a fast recovery TO220 model )
The schematic isn't correct in this case, the diode seems to be drawn wrong. However I will try moving the diode up to the motor. I will try to located a different diode...

1) place a low ESR 1000µF or + capacitor as close as possible to the motor ... to lower the 12v power source impedance. ( by the way, I'm saying the mosfet could be placed close to the motor ...and the diode between motor terminals ...)
The mosfet can't be moved. I don't know if I have a low ESR cap. I can dig through my parts bin. Anything specific I should be looking for?

2) place a .1µF on your motor terminals
Is this in addition to the above cap?

3) place a 10nF between each motor terminal and motor frame which has to be connected to circuit ground.
Will try.

4) you can place a core coil ( 1mH range "big value" ) in series beetween 12 v and your 5v reg input
I don't have anything like this lying around.