Bi-Amplifying Speakers using two B&K Sonata Ex 442

Active Crossovers from what I have read are the best approach to bi-amping because you don't share the amplifiers power between the speakers drivers. I believe I may have figured out a way to bi-amp using a passive approach but still gaining the benefits of the active crossover. By using two B&K Sonatas and a preamplifier that has two rca outs I will be able to give a full 200 watts to each of the drivers gaining the benefits of active bi-amping. The B&K Sonata incorporates two power transformers, one for each channel, at 200 watts each. By connecting both the preamplifier's right rca outputs to the inputs on one of the amplifiers I could then power it's hi/mid drivers with the amps right channel input and the woofer with the amplifiers left channel input. The fact that the preamplifier's right channels are going to this amp would mean all drivers are receiver right channel information each at the full 200 watts. The other speaker would be driven similarly by the other amplifier but using the left channels from the preamplifier. The end result would be a full 200 watts to all of the hi/mid drivers and the full 200 watts to the woofers. This would give all the benefits of an active crossover but handled through the speaker's crossover in a passive way, no need for the external active crossover. Does this make sense and will I be gaining the active crossovers benefits as I believe I will?
I vertically biamp too - pretty common, but does not accomplish (ie as you believe) what an active crossover does. It's true that both sections receive a full 200 w/c, but they are ALSO receiving the full bandwidth of your preamp (ie 20hz - 20khz). The active crossover will ONLY send bass frequencies to the woofer, and ONLY send mid/high frequencies to the mid/tweeter. Thus, each channel is only amplifying those respective frequencies. In my case it's not worth the expense of an active crossover, but if you're after a truly high end system you would have to do that.

I have tried passive biamping both vertically and horizontally in multiple systems and multiple amps, and there's only one case where I noticed a difference (still using it today). It's very speaker (and probably other components) dependent. Also, many argue you're better off not biamping but instead investing your $ in one better amp (ie than your EX-442). There's likely some merit to the argument, but I have not found one "better amp" for 2x the cost of mine . . . so there's that.

In any event - you already have the amps - go crazy with biamping.
Thanks for the clarification. I have one of the amps and was considering purchasing another which is on the market for a reasonable price. Your suggestion of upgrading the amp, is also what I am wrestling with. I now understand vertical, horizontal and active bi-amping better. Lots to mull over. Based on the best way still being active I believe my best choice might be a better amplifier. Thanks all for the input.
I helped a friend set up a system that consisted of 4 factory matched B&K M200 amps connected to the 4 balanced outputs of a SFL 3 pre into the dual inputs of Dunlavy SC IV's. The difference between and 2 mono amps and 4 mono amps, even through the passive cross-over was a revelation. YMMV.