Hi, John,
Good to see you on a board, long time no hear.
As you know, a transformer into the MM will be the quietest input, but may require a bit of experimentation to find the one most synergistic.
I have an Allnic head amp based on nuvistors, inevitably some tube rush in order to get the benefits of a very specific and deep soundstage over the built in transformers, which are completely noise free. However, as long as the cartridge output is over .3mV, I really prefer the head amp's sound quality.
I think you are describing a common dilemma with analog. I have come to regard the "noise companion" the necessary condition of the best analog sound, and have chosen to embrace it somewhat rather than fuss about it.
I had an Accuphase head amp shortly, still had some noise. You may get somewhat quieter performance with an FET, but I think it would dry out the sound and lose some "bloom" if you are coming from an all tube front end.
That actually might be preferable depending on how lush or bloomy the rest of your system sounds.
I think with cartridges at .2mV and below, that a transformer is really the best solution with whatever compromises it might entail. With outputs in the higher ranges, a head amp is a better choice.
Outside of the Allnic current production nuvistor head amp, which is expensive, the "vintage" Accuphase head amps are probably some of the best sounding and quietest available.