For me it would be an easy decision. The VK75SE to match your BAT preamp. I had a VK55 in my system on loan and it was fantastic.
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I've owned the Ayre V5xe and now own the BAT VK-55SE, but I didn't have them at the same time so never could do a side by side comparision. Like you I own the Ayre C5xe.
From memory I really enjoyed the Ayre amp but for what I listen to (Classical/Jazz/Vocal) and in my system I much prefer the BAT. No knock on the Ayre, but this is my first tube amp and I have no desire to go back to SS. I like the synergy with BAT tube amp/preamps and the Ayre C5xe is a very nice front end with BAT, IMO. ( I want to send my Ayre back for the 'filter ' upgrade.)
You're looking at higher end gear than what I have, but I'm sold on BAT. The 55-SE is all the power I need with my Harbeths. I've not heard the Von Schweikerts, but have read that they can be very revealing.. as you have the 31SE I'd be inclined to lean toward tubes.
Hopefully you'll get some feed back from owners of the "JR's" who have actually driven them with a tube amp.