best integrated amp.

Agree with the Hegel H300, have had mine for 2 years and it steps up to new levels depending on the speakers. I just demoed with Sopra No.2 and its the best the Hegel ever sounded. I like an Integrated that has the next gear when required. I suppose the Hegel didn't perform any better the Sopra's simply let you hear what the Hegel can actually deliver. That to me is a good investment piece.

I'd think you want to listen to the Primaluna Dialogue HP.  I have the amp, not the integrated, and it sounds amazing.  I think the integrated is in the low $4K range.

Impossible question to accurately answer. Synergy will make or break any individual component.

You might check out Vinnie Rossi's Lio, which is at the upper end of your range (ok, so a little over), but gets rave reviews.
http://www.6moons.com/audioreviews2/vinnierossi/1.html
http://www.stereophile.com/content/vinnie-rossi-lio-modular-integrated-amplifier#YfjbGTp5H9mXyGyf.97