Well, Greg, I recognize that quote so you know how I feel about the Diotima/Gastinel! The Raphael Ensemble is probably my favorite overall right now; the Pavel Haas Quartet's new album is superb too, but with sliiightly too reverberant sound. Of course, I am very very picky about recordings of this quintet.
What I have is...
Raphael Ensemble - totally excellent, heartfelt, in good sound
Auryn Quartet, Christian Poltera - technically flawless, but a little too "perfect" or perhaps insufficiently emotional
Pavel Haas Quartet, Danjulo Ishizaka - another top choice, hugely emotional journey, slightly reverby
Vogler Quartet, Daniel Muller-Schott - pretty darn good all around, probably my favorite that's on Naxos Music Library
Alban Berg Quartet, Heinrich Schiff - the sound is just too old and thin for me, and omitting the repeat is heinous!
Emerson Quartet, Rostropovich - just came in, waiting to be played!
Cleveland Quartet, Yo-Yo Ma - have only heard once, seems pretty solid
Belcea Quartet - bloodless, swift, do not recommend unless you're into that
Diotima, Gastinel - big, romantic, exaggerated, unusual but irresistible
Whoever the performers are on Vivarte - pretty good period instruments account, and can be had in a 5 CD box for about $15
Whoever the performers are on Fuga Libera, paired with an Arpeggione Sonata - I heard this a few years ago and liked it, but it's been a while
The Pavel Haas Quartet and Ishizaka live at Wigmore Hall in 2011 is the first time I ever heard this piece, so I may be prejudiced in their favor? But they really are excellent and that was one of the great concerts of my life. This could possibly be my favorite work of chamber music - and like you, the hunt for The Perfect Recording continues...