No worries, Jim! Keeps us sharp, and gives us something to discuss!
Check out yet ANOTHER THREAD that might help you understand the "diagonal biamping" setups more.
Crossovers don't necessarily dissipate heat from the power signal that isn't of interest. An ideal capacitor or inductor would dissipate no heat at all, and usually manufacturers try to approach those ideals since low heat generally means longer life and friendlier to use. Sometimes the resistance of an inductor is deliberate or used to advantage. Even shunt-connected reactive crossover components can't pass too much current, or the amplifier will be unhappy.
That said, there are often attenuating resistances and notch filters that *do* waste heat, and those can be reduced or eliminated by active crossovers.
Passive crossovers can affect the load the amplifier sees, for worse or for better. And passive components can block harmful outputs from an amp, so they can help protect drivers.
Passive biamping doesn't help the *voltage* headroom directly, but if the load is split between amps then their power supplies won't sag as much as a single heavily loaded amp would. It still spreads the current demands and IR and heat losses between amps, and reduces current-dependent distortion.
I don't follow you there, Jim? *Active* biamping sends different signals than passive biamping, of course.
If you leave the passive crossovers in place and connect the same way as for passive biamping, then the passive crossovers will *still* affect the signals the drivers see. Yes, the active crossover will be working, but so will the passives. The combined effect may not be optimum. Speakers are designed so the output of each driver is carefully controlled, especially in the tricky crossover region. That region may extend an octave or more on either side of the crossover frequency. Dropoff or peaking of sound from the driver, phasing, and directionality might not work out as well. The Pro approach is to use 24dB/octave (4th order) LR crossovers to get out of the crossover region as quickly as possible, which allows for greater driver bandwidth and power utilization and ease of positioning. But every speaker is different, so leaving passives in place might significantly change the sound.