I think you should buy the H120. Even the H90 would be fine, but the H120 would be a no brainer.
I tried 7 integrated amps in two months in search of my next best amp. What I found was that they matter the least. The source and the speaker make a much bigger difference.
Don’t buy the speakers first. You need to match the speakers TO THE AMP, not the other way. In your room size, the Hegel will do everything you need. Any 2-3K bookshelf speaker from Dynaudio or Wharfedale or alike would be a huge upgrade to the B&Ws