Now I see your problem. The issue is primarily stacked crossovers.
Those speakers have a passive crossover at 100 Hz to the woofers. I have to say this is a really bad design. Passive crossovers below 400 Hz are fraught with problems, and in my view are a never do approach.
Integrating these speakers with a sub is going to be a real challenge as you have found out. If you use your sub above 40 Hz you will have serious problems like you are encountering.
So: - you can not use DIRAC it will not be compatible with your system.
I would also switch off Audyssey for now. Set your system to LFE + main. There is no other way to integrate a sub with those speakers. Now so as to avoid crossover interaction you need to set the crossover to 40 Hz, as it needs to be as close as an octave and half below 100 Hz. 40 Hz will be close enough to avoid stacking. Now set the sub output until it sounds right to you. After that you can meddle with Audyssey, and it might help you. Those speakers have a nasty peaked bass response centered on 70 Hz. As I say there are more incompetently deigned speakers than competently designed ones. Those speakers have a "howler" of a mistake. So if you can't get the results you want, it is different speakers you want and not a new sub.
That is your problem and it is tough one.