Interesting discussion, folks....

As a controls engineer and High-Voltage electrician.... as well as
delving into HVAC control of late... here's my observations...

These manufacturers will always take the cheapest route possible and
damn the consequences. This is particularly true in power and control
systems.

A whole lot of manufacturers are moving toward PWM drives on their
blowers in particular. Many solutions are an 'on-board' frequency
chopper that is integral with the blower's motor.

These choppers are cheaply built and cheaply engineered. I suppose they
thought RFI and EMI would be insignificant due to the control being
mounted on the motor... but they're noisy as hell.

Suggestions: Replace the power cables with a shielded, VFD rated cable.
Belden makes a wide variety... I think they're called the VFD classic
line. Pay close attention the unit and cable grounding. Check to be
certain your house ground and neutral connections are only tied together
at the service entrance panel of your home.

My 2 cents...

Jake