OK, my circuit is in fact not out of the water. This one has me stumped again.
PIC is driving a pair of N-channel MOSFETs which make a half bridge for a transformer. The center tap of the primary is connected to +12v and it alternately grounds the other 2 wires. Standard and unremarkable half-bridge. The ground trace for the FETs and and PIC run in two different directions from the power supply ground, so there are no voltage drops that will affect the PIC. Same is true of the +12v going to the transformer center tap.
PIC is configured as an internal oscillator and set to 4MHz, RA6/RA7 are outputs. (OSCCON=0b11100010) MCLR is internal. Reg now has the correct capacitor on its output (actually 3x more). PIC has a 0.1uF ceramic from Vdd to Vss pins.
This is the problem. I ran it without the +12v wire connected to the center tap and I get the expected 62KHz frequency and 50% duty cycle on the PWM pins. The instant I connect the 12v, the square wave on the PWM doubles in frequency! Duty cycle remains the same. After a few cycles the PWM goes to 0 and I assume it's because the PIC reset, it keeps popping back up with a few more cycles and disappearing over and over. It's a bit more noisy but the PWM output is still clearly a proper square wave rather than some induced harmonic oscillation. As best I can tell the PIC oscillator just arbitrarily doubled itself. Remove the 12v power from the transformer center tap so the MOSFETs are no longer switching power and it goes back to 62KHz.
This is major weird. There's a bit of 12v and 5v noise, 5v goes down to 4.5v though I'm not certain why. All pins are outputs except for an ADC pin to read the voltage output and that one remains at a few mV. Electrically I don't see how the connection of a MOSFET load could relate in any way to the PIC so I'm stumped. Any ideas?