A couple of things come immediately to mind after hearing those files.
Firstly, I take it that this is a relatively new issue. If so, did they (your customers) install any new equipment within their facility (tower?) recently that may coincide with the start of this interference?
Secondly, when you did the sweep with the spec an did you try using it right in the same room where the customers' receiver is? As a subpart to this, locate where the antenna is an do a sweep right there as well - perhaps you can even connect the spec an to the actual user's antenna (during some appropriate time, of course) and try a sweep then.
To me, since you can't see anything on the spectrum analyzer when in the general area it sounds like it might be very local to either where the antenna is or where the radio receiver is. Possibly a new piece of equipment such as a computer or another radio. In fact, it sounds exactly like a heterodyne caused by a local oscillator leakage from a nearby radio receiver that is scanning between two or more frequencies (could they have a scanner or commercial radio that is in a scanning mode nearby?). But it could be a heterodyne from nearly any source very close to either the radio or the antenna. Try using a very short antenna or an RF probe with the spec an and sniff around the radio equipment and the area where the antenna is (if possible).
If the antenna is located far away and not easily accessable and you can't see anything on your analyzer within the radio room then try and find out if any new equipment has been installed nearby where the antenna is.
Also, be sure and check for harmonic sources - try looking with the spectrum analyzer at frequencies of Fc/n especially at odd values of n.
Also, be sure and check the power, data, and audio cable connections nearby and/or connected to the radio for conducted sources using an RF probe as the interference could be coming through those and not be easily received, if at all, by an antenna even close by.
And finally, a long shot but if all else fails - read the specs for the radio receiver they are using. Find out what the internal intermediate frequencies are for the receiver. Sniff around those frequencies with the spectrum analyzer as well, both conducted and radiated, as I outlined above. Make sure you check all IF's (if the receiver is triple conversion then look at all three, etc.). Leakage into the receiver's IF stages from external or connected sources is possible though a well constructed and shielded commercial aircraft radio shouldn't likely have this problem unless the signals were extremely strong nearby but it's worth a shot.
Just some suggestions - good luck!
-Mike