My Amp is good but probably the weak point

I recommend you revisit your setup first.  Setup accounts for a large percentage of the sound you hear.  Small changes in speaker position and any acoustic treatments can result in significant improvement.  
If your listening room is a shared space you may not have the latitude of a dedicated room but still might find improvement.

 I keep detailed records of speaker setup for each of my systems.  I recently decided to see if I could improve upon one setup I’ve been using for five years.  What changed?  Speakers moved three inches further apart, removed two acoustic panels, one diffuser panel, and swapped a water color painting with an oil painting.
Right now I’m happy with the change.  Sometimes one is just looking for change.  Time will tell if it was a sideways move or remain my new reference for this system.

There is not an amp that does everything. Same with Speakers, Dacs, etc. All because of system matching and integration. Synergy, is the word used here. YOU, as a listener, need to know what " specific characteristics " of recorded music, you are looking for. Lot of Klipsch haters here, but I am with you 100%, with that " Klipsch sound ". Imaging, refinement and presence ? Do you have your HIVs on the floor, or elevated on stands. I like my Heresy collection on stands, with no tilt back, away from the floor and walls. Try it. My best, MrD.

In other words, Massive stands, to get the midrange to ear height, and play with rear wall / side wall distance, and toe in. The Heresy 4 has a port on the rear, very similar to a pro model they produce ( ported, but on the front ). Very different design than Heresy 1, 2 and 3.The ports do interact with the floor, as do the woofers. I prefer them on stands, and sub bass, carefully tuned. I prefer Class A ss, because I want to hear WHAT the musicians are doing on the stage, before I hear where. Speed, agility, control, slam, detail, lower noise, and speaker matching ( when dealing with impedance and sensitivity ) are the major sonic attributes ss does better than tubes ( ime ). There are many tube amps that sound " luscious ", and some more than others. Some higher priced tube stuff gets closer to some of that ss, and vice versa. My tech builds tube products, and repairs all products. We understand each other, as to why he stays with tubes and I stay with ss. He is located in Central Florida ( Fine Tuned Audio /Video )....Kris is the man. Happy TG everyone. Always, MrD.

I looked at the list of gear and thought the same thing as many here, that the weak link here are the Klipsch’s and the amp is all wrong for those speakers. 

Sorry, I did not take the time to read all the comments here.  I know what I know, and that comes from 40 years in this hobby, with countless systems owned, hundreds of audio magazines read, and a few years selling audio gear at retail

jss49 is correct.  If the OP is glued to those speakers, than a SET amp will get the best out of them or even a SEP design.  The Odyssey is way too powerful for those speakers.  
 

A close friend owns an Odyssey Stratos amongst 20 other tube and SS amps and while they all sound incredible, he never thinks of selling the Odyssey.  It’s mated with large power hungary speakers though.

@stevehuff likes Pass Labs with the Heresy speakers and I agree.  Look for a Pass XA25