Whats the FATTEST sounding Tube amp to warm up Lean speakers?

Sure- the Jouls is known to be a favorite match by the designer, however, im trying to counter the speaker's philosophy here, so it is my thought that the Jouls is actually going to emphasize the leanness of the speaker, not counter it. Or Bobby P wouldn't have used it.

I for one would not characterize the Quicksilver midmonos as "fat" by any definition of the word but it very well may flesh out the lean character of the mid/upper bass of these speakers which is where the issue lies IME.

Agree, that many stock vintage tube amplifiers could be characterized as "fat" particularly in the area of bass. vintage McIntosh and Conrad Johnson certainly come to mind. I also concur with Rodman999999 regarding those vintage British tubes to help fatten up the presentation. I know a LONG time Merlin owner that went from Joule 100 watt monos to a Roger Modesky Music Reference RM9 after the demise of Joule-Electra. Last time I communicated with him he was quite happy, something to consider as well. 

Try a McIntosh tube amp.  Very warm sounding. 

The most popular speaker for many years with our M-60 amplifier was the VSM. Very nice match and we showed with Merlin at several CE Shows.

But I would not call the amplifier fat sounding (which usually describes an excess of 2nd harmonic distortion which our amps tend to lack). It just sounds natural. 

The Atma-Sphere OTLs and the Music Reference RM series of amplifiers are not going to "fatten" the sound, they are very flat and just get out of the way. As I mentioned on your other thread old Cary amps and as also recommended here old Conrad Johnson amps will be more suitable, but I also think you're not making the most of your VAC Avatar. Sure it's not  syrupy like some classic tube amps, but it is real. I can't see an amp speaker mismatch because Merlin speakers play well with lots of amps, but I'm not your ears either.