Improvement in Musicality for home theater system

Erik is right that all these amps sound radically different.  If you can find somewhere to listen to them, that would be best.  My thoughts:

McIntosh - if you want an engaging and dynamic sounding amp, this is the wrong choice.  The McIntosh amps are very laid back and mild.  If you pair them with a fast speaker, such as Wilson, they can sound pretty special, but in my opinion, it is still a tad laid back.  I walked into the Mac room at RMAF and they had the big monoblocks attached to Mac speakers and it was the most boring and dull sound I have heard.

Pass Labs - like I stated, these have a unique signature/texture.  Very refined and a lot of resolution, but the sound is very "controlled" (best way I can describe it), like it's on the edge of being exciting/dynamic, but just can't quite get there.  The XA amps sound a bit warmer/slower.

Parasound - I would not describe this as "syrupy" like Eric, but they are voiced just slightly on the warm side of neutral.  I have only heard tube equipment sound "syrupy" in the way it puts a glaze type of effect on the sound.  Also, the high frequencies have a dry type of sound (not my preference).  If you compare to Pass, the Parasound is a much more dynamic sounding amp, but lacks the high frequency resolution of the Pass Labs.  Parasound has incredibly clean sounding midrange.

Luxman - is a very high resolution/transparent and very neutral uncolored amp with lots of dynamics.  It really depends on what type of sound you're looking for.  There is a used Luxman L-507ux II integrated amp on usaudiomart for $5500.

Wow, this discussion went sideways really fast!!  so, based on this:

I was hoping to get some feedback on improving the musical delivery, basically more refined sound

I really think you do need to replace your Adcom amp.  I used to run these amps a long time ago.  While they were the "good for the money" amp and sounded nicer than the normal consumer electronics crap, they really are not that great.  Especially when you are pairing them with the Anthem AVM and the Revel M126Be (which is an excellent choice in my opinion).  The old Adcom amps were nice, but they were a bit warmer sounding and did not have good resolution at all.  Basically, the sound was a mess and you would not get good "separation of instruments" at all.

The new Anthem amps are not bad, but I think you can do better because they are not as engaging as other amps.  The Pass Labs amps are very nice, but they do have a unique sound.  Very smooth with excellent resolution, but have more of a "controlled" type of sound (i.e. they are not as dynamic as other amps).  If you like this type of sound, then great.  The "XA" Pass Labs models are "full Class A" and are even warmer and slower sounding.  Many love the sound of Pass Labs.  I would say if you wanted to keep the "type of sound" that you had with Adcom, but with much more resolution and refinement, Pass Labs is likely a good choice.

On the other hand, if you want a more revealing and transparent amp with a lot of dynamics, then I would recommend looking for a Luxman.  Maybe try to find a used Luxman M-700u amp.  There is a M-900u from The Music Room for $10.4k.  I don't know your budget.  Or you can go for a Luxman integrated for about $5-6k. 

There are a lot of Luxman products on ebay that are shipping from Japan.  I would be cautious of these because they are almost all wired for 100V  AC (Japan's standard) and will not work well with the 120V US standard.

I would try borrowing better speakers to compare your current speakers against -  using your AVR amp.

The resolution and transparency of the Revel M126Be speakers that he has completely out-performs his current Adcom amp.  Putting a better speaker in the system is NOT going to improve anything or give him better refined sound.  The Adcom amp is the limiting factor here.