How close are you flying to the antenna farm? The field strength
decays exponentially with radial distance. Put another way, as you
get close, you may be flying into a VERY strong field, outside the
design parameters of the radios your using.

The spectrum analyzer (if you can get one) will answer your inter mod
products question. You might make friends with your local HAM group.
Some of these guys may enjoy the hunt, an airplane ride, and have the
high dollar equipment to do it. But I'm betting that the cause
something simpler than that. The fact that you mentioned that they
were AM broadcasts reminds me of the times I used to get AM radio on
my telephone. In very high fields with amplitude modulation you can
get what's often called "detection by overload". Any non-linear
circuit element in your radio- front end through audio amp have all
kinds of semiconductors which can "detect" and demodulate the AM
broadcast if the signal is powerful enough. In the case of my
telephone, the bridge rectifier that protected the polarity of the
phone was the detector.

If this turns out indeed to be the case, and you need to fly your
plane into fields that are that strong, you might be able to get some
relief with improved grounding, sealing radio case gaps with copper
foil, a filter network right before the antenna enters the radio.