Used to work at a store part time that sold the NHT 3.3 and we used the McCormack DNA 1 and Aragon 4004 and 8008 on those speakers. The McCormack was definitely the better of the two, but the Aragon’s definitely gripped the bass on those speakers but the McCormack a more refined amp. Usually it was a DNA 1 Deluxe. If you’re not going to send a McCormack into SmC for the full monty upgrades which will cost you, expand your budget a little and look for a ARC 100.2. The 100.2 is a great amp that I think will be a nice match for your 3.3’s as I recalled can sound a little hot on the top so I’d avoid a sterile/cold sounding amp.
Definately moving out of your budget more, but the Parasound A21 would be a nice amp as well.