It would be interesting if you could do one of the above solutions at a time and narrow it down to which one or combination of the several solved it.

The 100uH coil going to ground isn't doing anything and could be deleted. I'd suggest only having one ground for the reed switch and shield preferably as close to the PIC as possible.

Did you choose the cap and the coil values for any particular reason? I'm assuming you're using a PWM controller and wonder if you could tune them closer to your PWM frequency to reduce spurious noise further. Usually I have many caps laying around and only a few coils so reducing your cap size would be the easiest.

Love the train.