I was interrupted while composing this post so forgive some redundancy, but I will include transient peaks in the discussion as I think they are relevant.
Irt the OP, let's look at the circuits involved. The HP portion of the speaker only uses a small amount of power to drive the tweeter and midrange driver in his room, even at reference level. As it is likely on the order of only a few watts any amp can easily manage that task. The LP portion of the speaker demands far more power to drive the woofer. Think of the mechanics involved moving that big cone and voice coil reproducing freqs into the subsonic range. This is the side that could potentially demand so much power during bass-laden transient peaks at reference levels that it could conceivably drive an amp beyond specs and result in clipping with audible distortion. But I kinda doubt that was happening at all when the OP originally had his nice Bryston amp hooked up to the speaker with the jumpers connected as I imagine it probably sounded pretty darn good.
Now, the OP removes the jumpers and uses the ext amp to power just the woofer and uses AVR int amp to power the tweeter/mid range driver. There is more power available to the speaker because two separate amps are connected. In fact, two separate power transformers are involved, one in the AVR and one in the ext amp.
But despite more power potentially being available, is more power being effectively used by the speaker? Certainly not by the HP portion. It wasn't using much to begin with and cannot benefit simply from more power being available.
So, how would adding the AVR int amp power to the HF side help? It doesn't seem to me like it will likely make much audible diff at all. If the system was formerly being driven beyond specs the amount of power now being offloaded from the Bryston to the Denon for HP side is unlikely to matter.
Let me say that those many of us who use a powered sub off the AVR's sub ch are getting some significant benefits due to use of true biamping in our systems. We employ an active crossover which creates a distinct line level sub ch signal for the LFs which is sent to the sub amp and a separate signal without low bass for the satellite speaker amp, whether internal to the AVR or external. Typically that xover is 80 Hz. One defeats the sub's built-in crossover or sets it to max so it is unlikely to have any problematic interaction with the crossover in the AVR. As for the speakers, one is not removing jumpers so the passive int xover divides whatever signal is sent to it as it normally would. That usually produces quite good results for most folks, even without any ext amp power or tweaking.
With Audyssey Pro, additional processing power is available so attention is paid to the effect of the room's acoustics and response of the sub and sat in the area of the "splice". The available crossovers are ranked irt smoothest predicted splice. That normally results in even better SQ.
A few dedicated hobbyists take it further, by using sophisticated room measurement systems to aid in sub placement, room treatments, even tweaking speaker/sub distances to further smooth the splice (and other portions of the FR in the room), all of which can result in measurable improvements.
I have ignored other debated aspects of passive biamping such as the controversial theory about woofer EMF effect on tweeter. Biamping is a pretty complex topic and I think detailed discussion would be best taken up on a more appropriate thread. IME it's far too easy for posters to get caught up in generalizations and absolutes when in fact there are many variables involved, and the many permutations of what's loosely referred to as biamping.
Edited by SoundofMind - 8/25/13 at 8:09am