Seems to me that you have both enough room and amplification for the 3.7s. I agree with Vhiner about the sub, the Thiel sub would be the way to go if you take that choice.
Since no one has mentioned it yet, again I'll venture a guess based on my past experience with the Thiel CS2 and CS 3.5 (as well, frankly, as in the cases of other speaker lines, like Dunlavy, when you went up the line to larger speakers), and see if anyone else can chime in. The big differences in the past between the two classes of speakers to my ears were both in bass quantity and quality and, more importantly, a better sense of ease in presentation from the bigger speaker and an overall bigger sound. The drivers moved more air, weren't working as hard and overall had a more relaxed and open sound, less strained. I know the 2.7 is really light years ahead of the CS2 and is probably one of the best Thiel speakers, but the 3.7 is a good deal better than the original CS 3.5, much as I liked that speaker, and is very highly regarded. I would think that ease, particularly in loud and complex musical passages, would be noticeable--it certainly was to me. If you listen more to smaller scale ensembles and music and at moderate volume levels, it may not be as important a difference. Just a guess based on past experience--I'm hoping someone who owns or has compared the actual speakers will add their two cents.
Since no one has mentioned it yet, again I'll venture a guess based on my past experience with the Thiel CS2 and CS 3.5 (as well, frankly, as in the cases of other speaker lines, like Dunlavy, when you went up the line to larger speakers), and see if anyone else can chime in. The big differences in the past between the two classes of speakers to my ears were both in bass quantity and quality and, more importantly, a better sense of ease in presentation from the bigger speaker and an overall bigger sound. The drivers moved more air, weren't working as hard and overall had a more relaxed and open sound, less strained. I know the 2.7 is really light years ahead of the CS2 and is probably one of the best Thiel speakers, but the 3.7 is a good deal better than the original CS 3.5, much as I liked that speaker, and is very highly regarded. I would think that ease, particularly in loud and complex musical passages, would be noticeable--it certainly was to me. If you listen more to smaller scale ensembles and music and at moderate volume levels, it may not be as important a difference. Just a guess based on past experience--I'm hoping someone who owns or has compared the actual speakers will add their two cents.