I have compared my HT-3 Plus (3 channel Stratos) to my Stereo Stratos, and the differences are subtle, and most notable on busy tracks and/or higher volumes. This comparison was done on a pair of Maggies, which are one of the thirstiest speakes of all - the more power they are given, the better they sound. I actually found the limits of the HT-3, but never have for the Stereo Extreme. I would say the benefits are tighter bass at all volume levels, and better detail at higher volumes. For lower volumes, and efficent speakers, the differences I think would be minimal.
I think the key is to do exactly what you have done: get into the low end of the Klaustronics amp line to get that special Indy sound. Then, upgrade the source, speakers, pre, cables, and then look into more Indy power.
I started out with a Stratos Plus, and everyone said skip the Extreme upgrade and go straight to Monos, but I had to learn for myslef. I recently pulled my Stratos out of my system in preperation for the mono conversion. It was replaced by my NAD T762 receiver, which is known for having very good amps (for a receiver). The difference was much more noticable than I expected. While the NAD sounded clean and clear, I instantly missed that warm, 3-dimensional sound.