Which 12AX7 tubes for EAR 834P phono stage?

The important issue is noise. you can only really use tubes tested for noise and microphony, by a really good reliable dealer RAM tubes are famous for this. As is Upscale and a number of others. Whatever flavor you decide upon they above all else must be quiet in a phono gain stage or in preamp gain stage.
The new or current production tubes are more often quiet tubes with no micophony than old stock but not as good sounding tone wise. The German tubes are known for being quiet and hatend to have a clean fast signal.
If you can afford good quiet ANOS Teles I would give them a roll.
The former Ei made a tube so lively and shiny it was called the silver bullet. Too thin for me but a fast sparkler, as the name implies. To get them now you must buy them as NOS tubes and believe it or not they aren't all that easy to find.
The current production, Russian Tung Sol gold pin for a straight forward sound leaning only a tad to the warmer side, has rich mid bass tone.
Haven't tried the New Blackburn tube yet but it seems to please those who have.
A brighter sound was part of what made the Shuguang 9th ed. or 12AX7C special. Yes I am serious and you can't find them any more. The B ver. or 8th ed. is what is being offered.

Telefunken will improve the low mid frequencies & Siemen will improve the tonal balance. It's your choice amongst the 2.

Good luck

As noted above, well tested, low microphonic tubes are required in a phono amp. better tubes can help, e.g. Siemens of Telefunken, but an 834p will never sound detailed or clear, at least, not without extensive modifications (with which I have no experience.) Lush and smooth, yes (in my system, too much so, just as you suspect.) But you have ss amplification, maybe it balances out. An 834P is a good place to start, but looking at the rest of your system, it is not up on the same level.

Another approach might be to try a livelier turntable. I use the 834P with a suspended sub chassis turntable and find the sound to be very dynamic.

If you want to put more money in to it (that you probably won't ever recover) and I think you would be far better of getting the coupling caps replaced and maybe a couple of other parts swapped out. Mitch the service tech for EAR USA has been doing these parts swaps for years and with the right parts you can get rid of the overly lush presentation. I think that is the more effective way of doing what you want compared to tube rolling, but I can't see it is the best from a economical point of view. You might be better off selling it and trying a different phono stage.