From what I have read, "VT-231" is nothing more than an inventory number used by the US Navy during WWII. All you can really infer from this designation is they were produced in the 1940's in support of the war. Evidently, they are identical to 6SN7GTs made during the 1940's for civilian use.
My impression is the Sylvania VT-231 is prized by those who combine more than one 6SN7 together to counterbalance deficiencies in each to achieve a desired sonic signature. But as your C3gs are very linear, and likely have no significant deficiencies, I believe they require an output tube with more balance than the Sylvania. If you are still interested in trying old-stock 6SN7, I would suggest a pair of Raytheon VT-231. There are two versions, and the one with 2 free support posts and flat plates seems to be preferred over the other. Or a pair of Tung Sol "Mouse Ears." In my experience, both of these have pretty good balance.