Resonance
Jon,
It sounds like what you have happening is resonance. When an antenna receives an electromagnetic/electrostatic signal, it induces a small current in the antenna. That current in turn induces a new signal. This is how parasitic arrays work (think old style TV antennas). By controlling the distance between elements you can control directivity and amplification.
I think this is what is happening to you. One antenna is receiving the signal, rebroadcasting it ever so slightly out of phase and it is them received by the other antenna. That also explains why it is more prominent on the ground, closer to a transmitter. I'll bet that if you had someone generate a test signal from nearby, and then were to rotate the aircraft you would notice a change in the "echo" as the phases between the antennas and the source change. Likewise, is it frequency dependent? There is about a 14 inch difference in wavelength between 118 and 137 mhz.
I think your best solution would be to relocate one of the antennas. However, I would double check all you grounds for your radios and your antennas, chassis grounds, shield grounds, etc. Perhaps set up a ground test like I mentioned before. While you hear the "echo", disconnect one of the antennas and see if the problem goes away. If it does, you have a clue. Now, you could try moving one of the antennas by pulling the cable thru the hole, try and maintain a ground plane, and move it around a few inches. See what happens.
Although the SL30 manual mentions ideally placing one antenna on top and one on the bottom of an aircraft, it didn't rerence a minimum distance. It did mention locating it as far away as possible from the ELT antenna, as there were some resonance problems with that with freqs close to 121.5.
It's all magic. You may actually have difficulty duplicating the problem on the ground. It's tough to troubleshoot something like that. Good luck, and let us know what you discover.
Don