I also do know about Fourier Transforms and I guess we have quite similar background (although I left the field a while ago).
Please don't misunderstand me, I am a TacT fan, I am using their units for about 6 years, I had/have the 2.2x, TCS 1, TCS 2, five S2150 and three S2150X. When you know the limitations of the product there are often ways to work around them.
I have been in regular contact over the years with many of the Yahoo forum members, yes that's true, on the forum there was a lot of controversy but the energy that some of users put in understanding the TacT units is impressive (some will even talk about reverse engineering). Please have a look to the TACS software (which was by the way sponsored by the official TacT distributor in europe), it is truly a nice piece of code and Boz himself was surprised the day he first saw it (I was there that day).
You can also wonder why these softwares (TACS, GV, Acourate) were developped... some users tempted by the adventure of active multiamping had the feeling they were too limited by the original TacT software.
However, these developments were a double edge sword, on the one hand they helped opening new possibilities (you will notice that TACS contains a 2150 firmware not available anywhere else, this firmware was actually developped by Boz to help them with this development of multiamping) but on the other hand this knowledge also revealed some issues here and there. This created heated debates to know whether these were bugs or features :-) At the end, when the new generation of hardware was around the corner, TacT took the decision to move all the computation back inside the units (as in the 2.2xp) which most likely close the door for future third party developments. Now we have no other way than trusting what is inside the box. BTW Lyngdorf took the same approach for their RoomPerfect system.