Swap out 12bz7 in favor of 12ax7?

I have not tried the 12ax7 tubes, but you can do it. I also have a V12R and have just installed nos 12bz7's. The amp responds well to changes to these and the el84's, as well as the power tubes. I just spoke with Mark at Cary and he suggests keeping the 12bz7 for the sound and that they are generally less expensive. As you probably know, the amps "R" status is based on the 12bz7 upgrade from the 6922 predecessor V12 amps, and the 450 volt transformers, up from the previous 375 volts. I am curious to hear any difference between the 2 different tubes if you do give it a try.
One other nice option with the V12 architecture is running it with only 4 power tubes. I have some matched quads, el34, 6L6, 6550 and KT77's which I have been able to roll around without spending several thousands of dollars for 12 tubes. Plus, it doesn't heat the house as much now that it is summer. In the winter though, it runs all 12 Tungsol 6550's and it thumps in triode mode.
Have you tried to under-bias the amp (10%-20%)? You may get the effect you are looking for.
Good luck and keep me posted. You have a fantastic amp!

Can you change the El84s to 7189's? A little less gain but usually a better sounding tube???

I suppose what I should have done in the first place is to call Cary and see what they had to say about it, so I did. Marc, their V12 guru, says that the 12bz7 and 12ax7 both have a mu of about 100 and so would have similar gain characteristics. To reduce the gain he suggests a 5751 with a mu of 70, or a 6027A (12ay7) with a mu of 40, and he went on to suggest that he really liked the sound qualities of the latter. He also tells me that the power supply upgrades that he installed in my amp this morning sound great and it's putting out a solid 120 watts in UL, so I'm looking forward to getting it back sometime next week. Will experiment and update.

I found most 5751 tubes to be a little "dryer" or less tubey than 12ax7s. Let me see what I have laying around for you.
Did you ask him about 7189 instead of EL84?