Int Amp for Thiel CS 3.7

Have you considered T+A? The PA 3000 HV?

Check out Pass!
https://www.passlabs.com/products/amplifiers/integrated-series

Pass Int 250 or Gryphon Diablo 300 ?
Which has the right sound signature for CS 3.7 ?

The question more should be which sound signature do you prefer.  The Thiels do a good job of reproducing what is given them; I can't imagine them not sounding terrific with either of those amplifiers.  Any way you could audition those amps to see if one has a sound you prefer over the other?

I presently use an Ayre VX-5 Twenty power amp with my Thiel CS2.4 and it has excellent synergy in my system. I recommend you consider the Ayre AX-5 twenty integrated as a match for the CS3.7