Need to learn about Audio Research

You should keep the H390 and add a Tube Preamp and/or even a Tube DAC like Primaluna. You’re not going to get better for less than $10K than the Hegel. 

I have a tube DAC, Lampizator Amber 3. 

Seems that adding a preamp to an integrated would be knda silly.
 

I don't think 100 watts of tube or SS power is going to cut it with 3.7s. I'd be looking for at least a high current 200 wpc amp.

I bought my ARC gear in the 70s after William Z. Johnson brought the SP-1 preamp and Dual 75 to Milwaukee for an audition. Those days are long gone!  We treated Bill to a prime rib dinner to thank him, and bought the units through Opus-2 stereo store in Memphis, Tennessee. At the time, I had KLH Nine speakers and later Infinity Servo Static -1s (with an ARC Dual 51 bi-amped driving the tweeters). Still have those amps and preamp to this day, along with a double pair of KLH Nines. Great sound all these years later!  ARC amps from that era are still available and serviceable by ARC. 

I just got back from the southwest audiofest-great show by the way- and the ARC Folks did a nice program on the history and future of the company. It was very interesting. ARC featured some brand new solid state products in its room that maybe haven’t even hit the market yet. Affordable pricing on these new products

I had 3.7’s a few years ago. As has been referenced I heard them at the dealers paired with ARC and they sounded great. That was indeed a classic pairing. I bought them but I couldn’t afford the ARC at the time so I went with classe integrated that sounded good but really didn’t have the power needed. I eventually bought a Pass int-250 which sounded lovely and had the necessary power to play these power hungry speakers. That purchase was started with reading I believe absolute sounds best of show review of the 3.7 with pass amps. I called Reno hi-fi which was the big Pass dealer at the time. He steered me to the Int 250 when I couldn’t quite pay for the recommended pass based on the review ( they were 16-18k ) and the 250 was around 10k.  It was a great choice which served me very well.You should get subs which will take the speakers to another level. You don’t mention a budget but you can find used integrated 250s for 4 to 6 grand.