Which integrated for Wilson Sabrina's

+1 on Krell.  Read the stereophile review by Jason Serinus.  I heard that set up on his system, and it was very impressive.

I realize this Vitus integrated is more than your desired price, but it’s about half its list price and may be a bit negotiable and should deliver just what you’re looking for. 
https://www.audiogon.com/listings/lisai451-vitus-audio-sia-025-receivers
I also heard BAT with an older pair of Watt Puppy 8s (I think) at a show it it also sounded really good, but that was obviously a long time ago but always left me with a feeling there was some good chemistry there.  Best of luck. 

Tweeters on the older Wilson models and on the Sabrinas are very different.
The W/P 8s that date back to mid/late 2000s used inverted titanium tweeter. Hotter sounding than the silk dome tweeter Wilson Audio implemented on the Sabrinas. With BAT you may end up taming a bit more than you intended.

Ultimately, home audition is a must. And unless it is possible or a decent return policy is in place, go used. You don’t want to drop this kind of dough blind buying a new component, end up not liking it and getting hosed on a resale.

I own a Gryphon Diablo 300 with Rockport speakers.  It is not edgy in any way and I can absolutely say it is worth finding somewhere to audition one if possible.   On the other hand a good friend has recently changed his system to a pair of Wilson Sabrina X and the Krell300i.  This is an excellent combination and I have really enjoyed my time listening to his system.

I second wsrrsw’s recommendation. Rogers High Fidelity EHF 200 Mark II. Quite powerful, great sound, very high build quality. I really enjoy mine. I believe you can try one & see if you like it. Call Roger & see..