Hello @andyknitt ,
I tested your model example with those two pins modified (PTB10 and PTB11) as I told you because I use an EVB. I didn't see any PWM signal on PTD3/PTD2 and PTE6/PTE2 (I used an oscilloscope to get the PWM).

If the MCU package used in your custom board is 64lqfp, then, as you can see in this picture the PTC6/PTC7 are near PTE2/PTE6 and not so far from PTD2/PTD3.
It is possible that you have some hardware issues (electrical coupled signals). In this case, the parasitic signal should be smaller than the original one and maybe rounded on the edges (it depends on the signal frequency and the type of the coupled type, and the impedances of the lines).
As a solution, if the parasitic signal is appeared due to a coupled electrical effect, you can try to connect a resistor on each pin that has a PWM signal that shouldn't be there(you can try with 10Kohm between GPIO pin and GND). This resistor should be enough to "consume" the parasitic signal. If this resistor affects the signal that you connect to the same GPIO pin, then you can try to adjust it. Anyway, try to not reduce the value of the resistor too much. If you increase the value of the resistor (higher than 10Kohm is not a problem as long as the parasitic signal has disappeared).
If that solves your problem, then a redesign of the PCB layout and maybe a schematic can fix the "ghost" PWM signal without using any additional resistors.
Please let me know if that works for you.
Best regards,
Adrian