This is the FM PLL unlocking!!! Many PLL's have serious problems with low bass frequencies, this is caused by the way of PLL works! Even, most MC145151 pll designs utilize the exact 12400HZ phase comparison frequency!
https://www.freescale.com/files/rf_if/d ... 5151-2.pdf
unfortunately, the problem lies within the design of your transmitter's loop filter. It is not sufficient to hold back that low modulation frequencies and then your pll unlocks even for a slight frequency, then tries to lock back on nominal frequency. That causes the artifact of some cycles of 12400hz to be audible. Consult your electronics engineer on the subject, he may be able to change some rather cheap filter components to accomodate for really low frequencies.
By the way, I have seen at least one design w. 145151 unlocking fully due to low frequencies, near 33 HZ.
By the way, you cannot afford swinging the modulation that much simply due to 30 hz signal. It's meaningless for most content since it kills headroom of frequencies more "normal" for music. So most FM transmitters have bandpass filter @40 Hz and this is why ST need to have one as well. I have mine set @ 60 Hz.
A perfect way to overcome the whole nature of those problems and still get bassy sound is bass boost. That would use the low bass input to excite harmonics where are audible via headphones and small loudspeakers, and there is a psychoacoustic effect that since you can hear those harmonics there MUST be the original frequency lying underneath, so your brain reassembles the sound.
Now, if you need to shatter some car's windows using FM, well, I am sorry but this won't work for your current configuration, unless you upgrade your exciter.