Need advice replacing my preamp

Haven't heard the BAT. 

I used to own the the PS Audio and it is wonderful preamp.  The stock tubes are awful.  It was shocking how bad.  I wouldn't have kept it for the year I had it had I not rolled tubes.  I used the NOS Tunsgrams that Upscale sells for this and they were very good.  I know there is a hot debate about what to roll in but just assume that you will need NOS tubes for it.  

I can think of another unit that is worth it in this price range but since you have it narrowed I won't bother  

I just linked to the Inamorata, the back panel shows only RCA inputs. I am not sure a jumper and XLR cables would solve your problem, AND long XLRs can get expensive

 My LS 100 has XLR outputs...

XLR outputs are not necessarily balanced. I have an LS 100. It is not balanced. It's one of the things in my system that I don't ever really think about replacing though.