Phono Pre Upgrade from Parasound JC-3?

I've heard that's a real good one.  Unfortunately it doesn't have balanced outputs.  I should have mentioned this in my original post.  The JC-3 has balanced outputs and when I switched to balanced cables after using standard RCA I was blown away by the improvements.  

I'm looking at the BAT VK-P6SE as it checks off the boxes and has great reviews.  Also consider a Manley Steelhead.  

I got a BAT VK-P6SE I'm going to try.  If I don't like it I can return it so there's no risk.  Always wanted to audition one.  

@lewm I use the balanced cables between the JC3+ and a Lyngdorf TDAI 3400 amp, which is also balanced.   

Update:  I hooked up the BAT VK-P6SE yesterday and listened to three record sides before unplugging it and packing it up to be returned.  
I'm thoroughly convinced that it's not a good match for my system.  The JC3+ blows it away.  I have to believe this is more to do with the robust loading and gain adjust-ability of the JC3, and the lack thereof in the BAT, but beyond that, I just know it's not right for me.