I have no conflict of interest to disclose. Tubeseller.com a dealer I think sells 6SN7S exclusively, has a lot of information on his site. He has credited a very long thread from the headphone site hed-fi.org which he abstracted. You would do well to read them. The other sites that I recall which have the general info you want are vintage vacuum tube services, and Brent Jesse's site which has a new name. Mr. Behr is quite knowlegable as a collector of 6SN7s amongst other things and I have benefted from him. But I don't think he has a BAT. The differences between the sonics a tube roll will make depends on many variables. Some amps don't respond or very little for instance my SP6B ARC preamp is difficult to manipulate. That said there are tubes which yeild a particular sonic signature on no matter what system it is used on...e,g. A Ken Rad 6SN7GT is very bassy.I am sure Victor at BAT will recommend a Russian tube.
I recently bought a bunch on N7s to a friend's place who has a Supratek. He settled on a very immediate, quick and a slight mid bass emphasisizing tube, the Sylvania 6SN7WGT. You may want a richer tone? The list is endless as youn already know.