Bi-Amping Possibility, which direction ?

If you get a xover, make sure you know how to properly use it, or have someone hook it up for you that knows what they're doing. Like anything else in your chain, an improperly used piece of equipment (expensive or otherwise) can and will do more harm to your system than good.
It would also do you well to find out more about bal. vs. unbal. configuration; find out if it's something you should really sweat over.

Nice speakers........a customer has a set.

Lots of dumb questions come to mind, like do you know the order, alignment, and, of course, crossover frequency of the speakers?? Simple passive balanced crossovers can be built. Emphasis on simple. Depending on the type, you may not be able to easily do it passive. In which case, balanced may be a pain to do. Tricky crossovers are best done single-ended, and you convert BAL-SE-BAL with a bunch of active components. Like Apogee did on one of their set-ups.

I think the trick with the Extrema is that it uses a coil to shunt the HF to ground for the tweeter. Could be wrong, but I seem to recall someone in the know telling me what was different about those speakers. But that was years ago.

I'm affraid that you'll only have a chance to play with biamplification with no success or even decrease your system quality...

I would try bi-amping without a crossover first. Use the coax to the threshold and balanced to the pass. Then, switch to balanced for the threshold and coax to the pass. See how it works before you knock it.....then tell us what is lacking. Your system should sound amazing!

Well if lateral is the way your going you have to have one so why not the venrable Brsyston?I think it does not even come with RCA's you need cheater plusgs to make it work.Not sure that other big company Marchand has XLR's but they have sooooo many models/config's I assume it is the case.
Chazzbo