Best mellow sounding 12ax7 for Thor TA-1000 preamp

May I suggest that you look at 5751 tubes. Slightly lower gain but much cleaner.
They are a direct replacement.
Google "Joe's Tube Lore" for a nice review of many different brands.
While your and my results will vary from those of Joe's, it is a good general starting point.
You could buy several pairs and try them to find what best fits your system and then sell those that don't float your boat.
A very good one with a bold presentation and rather sweet treble is a Raytheon 5751 with the windmill getter.
Good luck and Have Fun with it.

New Production Mullards can do what you want quite nicely. On a budget that is what I would (and do) do.

NOS RCA 12ax7 cleartops would fill the bill. As would the Raytheon 5751's mentioned .

I have to agree with vintage Mullards (haven't heard the new Russian ones) and 5751 especially the RCA black plate.

RCA 12AX7 or 5751 BlackPlates have smooth, open sonics. A classic tube sound, less expensive than Mullards.