NOT likely to DeTune the fretless six, especially when it uses a 2TEK brdige which prohibits DeTuning, but what you are suggesting reminds me if the Picollo Bass.
Having just typed all that, it occurs to me that maybe you could re-string and re-tune so your lowest note is higher than F. Say, F# standard or G standard. Get up above that problematic resonance. With the right bunch of experimental bandmembers, that could be fun to explore. Find a drummer who uses a small kick, and somebody that plays tenor guitar, or some brass...In the right context, it could sound interesting...let that cab’s limitations or idiosyncrasies be an inspiration in a new direction. Hey, Mark Sandman and his two-string slide bass (tuned D and A, I think) did some cool stuff with baritone sax and drums in the band Morphine.
EDIT: I am pretty far off the “how do I fix this cab’s issue” here but I’m not making fun. Trying to think outside the box, so to speak. See what I did there...Anyway, you’ve mentioned having other rigs, so if the F-Bomb turns out to be an unavoidable acoustic “feature” of this cab no matter what, this is one way you might be able to keep it and have fun with it without the resonance F-ing up your playing fun.
I have a Bag End 18 which does fairly well. Probably I will simplu get the Rolls RPQ, and when combined with a Dyna Comp, I will be able to pretty much Surgically Remove and Flatten Out the F Bomb.
I am NOT going to worry about it.