Not necessarily -- the simple upshot is I don't have a plan.
But as I understand it: You are taking the sound output from the speakers ("stereo out") on the GP35 -- sending that over the air by RF (FM), and capturing it on the other side with an FM receiver. Sending that through the stereo, and subwoofer. As I understood it, the resulting frequencies were missing the "low end" from 300 hz down which you discovered. You then used the Mooer to move some higher frequencies down into this range with good results.
So I wondered if the original sound files had these lower range frequencies. I've been guessing they are there and instead are filtered out by MTH "audio processor" for whatever set of reasons.
I'm also guessing that "ideally" for what you would like, you'd like a "line out" off the board so that you get the "pre-filtered" right from the sound file frequency set to do with as you see fit. My way of thinking is that ideally you don't really want "stereo out" but "line out" with all the frequencies present in the sound file. Well, we can ask them for such...
But given all that, I thought I'd look in the sound files themselves to see if I can determine what is what. I thought it might be interesting to capture these various sounds and also to try to extract the low frequency sounds from them as well. There's several things to do there, one of which is to see what it all sounds like through my own stereo/subwoofer... and I don't mind sharing the sounds clips I create in the process ...
Beyond that, I don't really have a specific plan exactly -- although I'd like to replicate your set up on my SD70ACE or maybe I need to buy a junker I don't mind burning up... (or ... ?)
I can also think of a complicated things to do with the clips but its not clear the results would be better... (or even work)