It might be best to ask REL about whether timing issues would be a concern in the scenario you are envisioning.
Regarding the radio station interference, I suspect that could be eliminated (with no audible side-effects) by putting an inexpensive ferrite clamp around the wires from the existing sub, probably at a point near where they are connected to the amplifier.
I would suggest that you take a look at the ferrite clamps listed
here, and select one having an appropriate inner diameter.
If you can hear intelligible audio from the radio station, I suspect that it is AM and not FM which is being picked up, in which case you would want to select from among those listed under the "Low Frequency 200 kHz - 30 MHz" tab on the page I linked to. If the interference is other than intelligible audio, and/or you somehow feel fairly certain that it is indeed FM, select from among those listed under the "Lower and Broadband 1-300 MHz" tab. Or perhaps buy one from each category, and try both.
Assuming that the interference is being heard from your main speakers, and not the sub, I'm envisioning that the radio signal is being injected into the feedback loop of your amplifier, and its AM content is being demodulated as a result of non-linearities in the amp. Which is why I suggest putting the clamp near the amp end of the cable.
Good luck. Regards,
-- Al