Bryston with vandersteen.

I had this exact same setup a little over a year ago.  Same amps and exact same speakers. I found that vertical bi-amping was better in my room. 
I really loved the 2CE sig II‘s. What a great speaker. 

Since that time I have moved on to a different amp and speakers, but it was worthwhile at the time. 
I used the audioquest splitters. 

See p.3 of the 2CE manual, where it also has a diagram:

https://www.vandersteen.com//media/files/Manuals/2ce_signature_ii_manual.pdf

Try it ;-)
see the model 2 manuals, free download online for do and don’t 

The two (L/R) channels should be exactly the same.
IMO - It would be more useful to compare ^that approach^ to just bridging the amp. Which was the counterpoint I made earlier. I think it is worth trying both your Bridged-mono idea, as well as the upper/lower stereo.

To really get more advantage from bi-amping it could be useful to have the bass frequencies removed from the MR/Tweeter channel. Then that high freq channel has a lot more voltage headroom. However that requires some active filtering to happen between the preamp and the power amp.

Any analogue approach will alter phase, and the only digital approaches that would not alter phase are FIR based using symmetric filters. But that sort of goes somewhat orthogonal to the 6dB/octave crossovers in a Vandy.

Using a Vandy sub requires the Vandy crossover, which also is scraping off the bottom content which has the high voltage excursion. Conceptually it is similar to what we are discussing… and probably a better and more easily heard improvement over using two amps to power the speakers??

Or maybe both (sub and 2x amps) are most optimal.

@knotscott  thats an interesting way to do it. Then play around to see wich channel left or right would be best for bass or treble. Sounds like something to do this weekend.

Assuming you have two identical Bryston amps, I’d look to run a passive vertical bi-amp configuration using one 2-channel amp per speaker. One channel of each amp the woofer, the other channel for the mid/tweets.

The only expense is another set of speaker wires, and possibly a method of splitting the source signal at the amps. You’d gain the benefit of having zero left/right crosstalk between the amps, which helps with soundstage and separation (as would running them as monoblocks). Plus the mid/tweeter channel benefits from not having the burden of controlling the excursions of the woofer, which in theory lends to better clarity.

...maybe try both bridged and bi-amped to see which you prefer.

Alternatively, one could also run the pair as stereo on each side, with the L/R sides bi amp to the speakers woofer and MR/T bi-wire posts?
How much power, or voltage do suspect that they are receiving now?Or how much SPL are they delivering?