Speaker choice for BAT VK3xi/VK250

I have the same equipment as you, and just purchased Montana EPS 2 speakers used for 5k. They sound very good and the amp is not broken in yet.

Don't know about the other speakers but VK-250 and Maggie 3.6 are not good match.

I used a BAT VK-300SE with Rega Apollo and Thiel 1.6 speakers (HT magic IC and Pro-9 cable).
This combination yielded the finest sound I've had in my home.
Felt I was hearing 100% of the musical intent on everything but the most poorly recorded disks.
Super low noise floor also.
Synergy? Don't know or care.
Sadly, I sold the BAT and Rega thinking I would soon be unemployed.
I'd try some Thiel CS6 speakers in your system.

Having owned Magnepan MG3.6 and have Demoed Dynaudio 5.4, I purchased and like better Revel F52's. So my recomendation is a pr of Used Revel Studios you can get them for 5k

Save some of that cash and try the Vienna Acoustic Beethovens. I had the VK5i and VK200 with those and it was great!