When you ask for input for an upgraded integrated to match your speakers, you would hope that you would get feedback on what amps would work with your speakers, not just amp feedback. I had your speakers over 20 years ago and not just any amp will work with them, it doesn’t matter much about the efficiency of the speaker to some degree.
With your nht’s you have 2 parts of the speaker that I treated differently, the speakers on the front and the 12” woofer.
The NHT tweeter is a metal dome type and you need a warm sounding amp to tone it down. If you look at most smaller tube amps, they will be fine for the front panel speakers but will not control your woofer, your will get more sloppy bass and the volume won’t be inline with the other speakers.
My suggestion (I actually did both ways) is to get a good quality tube amp or warm sounding SS amp for the 3 speakers on the front baffle (maybe the rouge Cronus magnum with the kt120 tubes or a McIntosh 6500 type integrated) and then get the nht’s sa-3 amps for the woofers with the volume control to match woofer output to the other 3 speakers. In a small room, it’s tough to get the woofer output to match the output of the other 3 drivers if you go with a under powered amp, which brings me to my other recommendation:
Get a large warm sounding amp that will control the woofer and tame the tweeter. The McIntosh 6900 was a good fit back when I had the speakers. I also went the separates route with the odyssey monoblocks with a classe preamp.
Goid luck