Bi amping with two different pairs of monoblocks

The whole proposition is ridiculous. Does anyone really expect two $5k speaker cables to sound better than one $10k one?

The amp powering the tweeter needs to deliver a miniscule load, it's not worth it.

I researched this subject extensively and unless you have exhausted every other option to squeeze out the last drop of resolution, forget it.

You do need some sort of gain control to balance the amps .some amps have the gain control on them. I have systems that are tri amp and quad amped. These are line arrays have many speakers like infinity irs v ect.make sure you check on manufacture max wattage per channel. Match that with your amps.enjoy the hunt.

Every case is different.  I don’t agree that it’s a ridiculous proposition.  It depends on several variables. 

In my case, the Dynaco/VTA monoblocks benefitted from seeing an 8 ohm load vs 4 ohm, and also benefitted from not having to operate in the lower octaves.  Bass improved from the solid state amp too.  YMMV, but you’ll never know til you try. Good luck!

Another option would be the Dayton Audio DSP-408 or something similar. It gives you 4 channels in and 8 out and a multitude of controls, including volume and crossover . It's $179. It's overkill, but will work. Besides, you can play to your heart's content. 

As mentioned level matching will be the issue you need to address between the amps.  An external crossover is the best way to address this.