You are correct, bi-amping is the way to go. I have been bi-amping my Big Stereo for decades now, I would not have it any other way. I also agree with tri-amping, although that approach is less common as it is expensive and the improvement is not as significant as bi-amping.
However, there are some issues to get right. First, you don't need equal power for the two amps, what you do need is equal gain. 80% of the power is in the bottom 3 octaves so, generally speaking, the top 7 don't need as much power. There are exceptions, the impedance dips in the top 7 octaves may require more current, hence more power. If the impedance in the upper frequencies is higher, then it will require less current to drive them.
If you split the passive crossover inside the speaker, it has to be designed with that thought in mind, as all the impedances interact. If it was not designed that way, then you will have to use and external, active crossover. There are some available, cross it at the same frequency and slope as the passive unit.
Either way, you will have to add a second pair of speaker terminals and fusing for the second amplifier.
As long as the gain is matched between the amplifiers, you can also do creative things like using a tube on the top end and solid state on the bottom, which is what I am doing.
A call to the speaker manufacturer will answer the question of the impedance curve and whether the crossover was designed for splitting.