what tubes for eastern electric minimax phono?

Check out Cryoset's website.  Ron Sheldon's Cryoset offers several fine brands of 12AX7s.  I consistently enjoy the cryo treated Gold Lion tubes.  Very quiet neutral sounding tubes with nice dynamic swing that stay quiet for a long time.  I'm sure Ron would be happy to discuss his tubes with you and recommend tubes that would most likely deliver the sound you are striving for.

It depends what sound you are after. Subjectively a lot can depend on you and your setup.

NOS Telefunken EC83 is low noise and neutral. From current production, Gold Lions are really good too. Both are reasonably priced ($50 or so). These should be equivalent or better than your Tung Sol. Fantastic clarity and detail with tight bass. Ideal for classical.

For sweetspot warmth, try NOS RCA long black plate slant D getter from 50’s. These have warmth in spades but retain resolution with sparkly highs. Ideal for rock, blues and pop.

Warmer still would be NOS Mullard but you can expect to lose some resolution. Kind of dark.

@shadorne +1  It seems apparent that you know your tubes.