Thought I'd give everyone an update. I have purchased a mint-condition Conrad-Johnson Premier 350SA amplifier. It is, without a doubt, the best amplifier I have heard with the CS 3.7's. It bested Bryston, Sanders and Classe's latest stereo amps by a clear margin.
Everyone who's heard it in my system is impressed with the bass, soundstage and layered sound stage. I suppose it helps that this amp is mated with a CJ CT5 preamp. To my ears, the 350 SA lives up to its legend. Martin Collum and Jeff Dorgay are spot on about its strengths and prowess. At 600 watts into 4 ohms, it is utterly undaunted by the 3.7's and manages to lift their considerable load with musical ease. Bass is deep and taut and highs are silky and seductive. One friend said, "I never knew what the Thiels were capable of until now." The 350 doesn't sound exactly like tubes, but it's 95 percent there. It definitely belongs on the "must try" list for 3.7 owners. Some at Conrad Johnson have said the 350 could not be made today for less than $15K. I have no way of knowing if that's true, but it sure beats the new $9K amps I put up against it. Must be all that Teflon!
I never could audition a VAC or the Hegel 30. Maybe one day...
Thanks to everyone for your suggestions.