The IC-RP1510 receiver looks like this (everything in MHz).
 
 146.145 1st 21.8 2nd 0.455 demod and
 RF in ----> Mix ---> IF----> Mix ---> IF ---> RX audio
 | |
 | |
 5.12 ------> 124.300 21.345
 Ref Osc 1st LO 2nd LO
 
There is also the 146.745 transmit frequency, and 91.1 FM broadcast 
station frequency involved.
 
This time, I think I found the intermod mechanism. As usual, 
nothing is simple until the answer is found. Then, it looks easy.
 
It's called "Half IF" and it's about as obscure as it gets.
http://www.radioing.com/eengineer/rfi.html
What happens is that an incoming signal (as generated by an 
intermod mix), mixes with 146.745 transmit signal, to produce 
one half of the 1st IF frequency. The half IF is then 
multiplied by two in the fist mixer, to produce the 1st IF 
frequency, and ruin my day.
 
The half-IF frequency is:
 146.145 - (21.8/2) = 146.145 - 10.9 = 135.245
 
This frequency is produced by the IMD mix as [1]:
 TX-freq - (3 * 1st-LO) + FM-station =
 146.745 - (3 * 124.3) + 90.910 = 135.245
 
The 1st LO then mixes with the spurious 135.245 signal to 
produce:
 124.3 - 135.245 = 10.945
 
The 2nd harmonic of the above mix lands in the middle of the 
2nd IF as:
 10.945 * 2 = 21.89
Close enough considering the bandwidth of the FM broadcast 
occupied bandwidth [1].
 
Unlike my previous guess(tm), this IMD mix has all the necessary 
components. It involves both the repeater TX frequency and the 
FM broadcast station. It does NOT involve any clock oscillators 
which is unlikely due to the repeater shielding. So far, it 
looks right.
 
The 1:1 relationship with the transmit repeater TX frequency 
explains why there was feedback squeal and why it was NOT over-deviated 
feedback, as it would be if it were a multiple of the TX frequency.
 
The fix is fairly easy. Get the FM signal out of the repeater receiver. 
Exactly how to do that will require some sophisticated testing 
(i.e. trial-and-error), as well as building a suitable FM notch filter 
(i.e. cut-n-try). A spectrum analyzer isn't going to help much. 
Since the mix involves the 1st LO frequency, reinstalling the RF 
preamp that's sitting next to the repeater might be possible.
 
[1] Note that the FM broadcast frequency that I used is not
91.1 rather 90.910. That is within the approximate occupied
bandwidth of an FM station as calculated by Carson's Rule:
 Occupied Bandwidth =
 2 * (deviation + max_audio_freq) = 2 * (75Khz + 53KHz) = 256Khz
The 53KHz is the highest modulation frequency without RDS
and SCA sub-carriers.
The range of occupied spectra would therefore be between:
 91.1 - 0.256 = 90.84 MHz
 92.1 + 0.256 = 91.35 MHz
http://www.axino-tech.co.nz/documents/Bandwidth%20needed%20for%20FM%20broadcasts.html