dejayos
There are generalities of course between 12AU7 family compared to the 6SN7, but here are mine; and I have both 12AU7 and 6SN7 systems in my collection. These are my own findings, others may disagree:
6SN7 - I find these tube components to be richer, fuller, smoother, sweeter, engaging, and a little (just a little) more relaxed with a large soundstage
12AU7 - These tubes are more holographic, precise, analytical, detailed, and dynamic
I own both, because they are generally different; and have their own place in my system....and can match better in different circumstances. In your case you requested help with a warmer presentation to smooth out your speakers, that would be the 6SN7 in my experience.
That is why I recommended Aric Audio, Supratek, and Don Sachs/Lynn Olson Raven preamps; their preamps are 6SN7 based (with some variations available). They all make state of the art (as much as tubes can be) preamps, are hand made point to point, EXTREMELY high quality components, and some (Aric Audio) can be customized to your taste if need be.....whether that is with different capacitors, tubes, or connections.
I personally own several Aric Audio components, so make of that what you will....personal bias for sure. Though I know of several people with Supratek and Don Sachs gear, who adore their equipment