What phono pre am I looking for?

Since you like tubes, check out Don Sachs' custom phono stage.  I have one and it is quite good, albeit MM only.  It can be had right at about $1k.  You could use a Decware SUT or have Don add a transformer for step up for less money. 

Either of those options limits future cart changes to similar cart output.  Getting a Bobs Devices SUT with a couple of gain options is more flexible, but of course more money.  The Don/Bob combo is what I use and I'd have to double the investment to get getter sound.  

BTW, I also have the LTA MZ2 preamp.  Don's phono stage mates with the MZ2 like a glove.

I do use a couple of MM carts that I like with the Sachs phono stage.  I simply bypass the SUT and Don's unit allows full tailoring of the MM loading.  Don has been really helpful with recommendations for the loading settings for the specific carts I've asked him about.

I even don't use the 47k Ohm default when using the SUT.  Again, Don helped me with fine tuning the MC carts when coming from the SUT.

@jmolsberg, a friend has the JC3 phono stage and we compared that to Don’s one weekend. They are different but I think comparable in quality. The JC3 clearly sounds SS where Don’s does sound like tubes in comparison.

The Sachs phono stage is really clean, not lush sounding. You said you were worried about too many tubes. I mentioned I have the LTA MZ2 that you have, and you know how clean, not tubey that is. I also have the LTA ZOTL40 amp, so I’m tubes all the way. If I had a bunch of iron core transformers and/or coupling capacitors mucking things up, I might have too many tubes, but the LTA gear avoids that thankfully. I have upgraded all the tubes with NOS that I think brings out the best.

I used to have a Cary SLP 98L, with the included phono stage. That was tubey sounding, which I liked but I didn’t realize how much was being muffled by that unit. Don’s phono stage took me two or more levels higher in quality from the built in phono section of the Cary, and you know how good the MZ2 is.