Balanced cable for a BAT vk3 - recommendations?

I picked up a Harmonic Tech Pro Silway II XLR for a song and it's insanely good. If you insist on spending more, go with Nordost Quatro Fil.

If you are considering the AQ Amazon, look also for AQ Diamond X3 or (if you can find it) AQ Diamond Extreme. Pretty close to the Amazon, and pretty "reasonably" priced in the second hand market. I use AQ Diamond X3 in my system, which is built around a BAT Vk5iSE

I second Audioquest. They work well with BAT.
Dragons are great, but definitely out of your price range. Find used Emeralds or Opals. They are under 150 /pair used. While you are on that consider changing those dreadful Mit2’s to something decent.

I would replace one cable at a time. You must think of them as another component. Siltech--very detailed, smoooth and very full bodied. I was using Cardas Golden Reference and much prefer the Siltech.

Yes, better grades of Siltech (expensive) are nice with any equipment. Newer AQ is excellent, and more reasonable used, but the older stuff just wasn't as smooth.