NICE 6922 tube that is warm vs cool

I guess you've visited "Joe's tube lore" at aa? If you want some midrange magic and not rolled off extremes then the tube you already mentioned Amperex 7308 I thinks is the best overall but if all care about is mids then telefunken 6922 followed by Mullard 6922.

I like the Telefunken Falcons. I use them in my Kora Hermes DAC.

You have already mentioned them tube you are looking for: Amperex JAN 7308 made in USA.

It is difficult to talk of how a tube "sounds" because the same tube sounds different in different circuits. Perhaps if you told us what product these tubes would be placed in, this would help us to give you a recommendation. Not knowing that, IMO, Telefunken 6922 tubes offer more of the characteristics you are searching for than any other tubes that I have tried. They are extended, particularly in the bass. They have great smoothness through the entire frequency range. High frequencies are sometimes less prominent than with other NOS 6922's, but don't confuse this with lack of high frequency extension. I find Telefunkens more neutral rather than warm, but they are certainly warmer than many other NOS tubes. Mullards, on the other hand, have much more midrange emphasis and punchy dynamics. I don't find them quite as extended in either the bass or highs as Telefunken tubes. Where the Telefunkens really shine is soundstage. No NOS tube that I have tried produces the broad and deep soundstage of the Telefunken and I have tried various varieties of Amperex, Philips, Siements and Mullard. My experience with NOS 6922's was developed with my CAT Ultimate and to a lesser degree with my Kora Hermes 24/192 DAC, but let us know what equipment you will be using them in. Perhaps someone with specific experience with THAT equipment can give you a more precise answer.