That said, I think separates are somewhat jumping the gun at this point as they get considerably more expensive so you might do well to start with a good AVR and go from there. I wouldn’t have recommended a separate amp at this stage since your new towers are very efficient and don’t require much power, and given that and as your system is primarily for HT it’s probably more important to match the amp across the front three speakers than giving the front L/R speakers more power.
Toward that end, if you do end up keeping the Adcom (which I likely wouldn’t) I would not recommend a Marantz AVR as its sound tends to the softer, fuller side than the more neutral character of the GFA 555. My best AVR recommendation, if it has all the features you need, would be the Yamaha RX-A1070 that can be had at Accessories4less.com for $640. It has plenty of power to drive all your Klipsches and would likely be a better sonic match for the Adcom if you decide to keep it, and it’s the cheapest model in Yamaha’s Aventage lineup to use a power transformer. I worked for Magnolia for a while and got to directly compare all their AVRs, and sonically I found the Yamaha Aventage AVRs to be the most transparent and closest in sound to my $25k dedicated stereo system at home. I used an Aventage AVR to demo revealing $9000/pr. B&W 804D3s and it impressively held its own even at that high level, so I’d think it’d also make your similarly revealing Klipsch sing very nicely. Further, and significantly, Yamaha is one of the most reliable mass market AVRs out there. BTW and FYI, Pioneer was bought by Onkyo - one of the least reliable AVRs - in 2015 and then was bought again by a Chinese private equity firm about a year ago. Nuff said.
So, if I’m you I’d see how your system performs with the better AVR and the Adcom and see if the separate amp is worthwhile at this point. Not to go too far off in another direction, but if at some point your new affliction spreads to include wanting better 2-channel performance then looking for a separate stereo amp and preamp (or good stereo integrated amp) starts to make much more sense as you’ll want both the AVR’s preamp and amp sections completely out of the loop for critical stereo listening. Of course at that point you’ll probably want to look at better speakers, and so it goes with this wonderful disease. Similarly, I wouldn’t consider a separate A/V prepro until you’re ready to spend multiples on much better speakers as well. Anyway, hope some of this makes sense and is somewhat helpful, and best of luck.