I would post this question over at AVForums where you're far more likely to get good responses. Mostly a 2-channel community here.
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For receivers, two options to look at would be Anthem MRX1120 for highest resolution and detail. Or look at Marantz SR8012 for a more warm sound with excellent sound quality.
Ultimately, separates are a lot better, it is going to be hard to get a good sound quality HT Processor that also supports 4K. You could try looking at a Marantz AV7705 (or previous generation AV7702) and the fine a nice 5-channel amp.
Many might think different, but in my opinion, Denon is very similar to all the other conventional receivers (onkyo, pioneer, sony). Yamaha are not bad sounding receivers - they are at least more natural sounding. The Denon has a very solid-state sound with that solid state "edge".
I think the Anthem receivers are the best sounding and highest resolution AV receivers that are available. However, they can be a little bright in some systems (though not nearly as bad as Denon). You can tame this using gold-plated connectors on speaker wire / power cords.
Your Martin Logan Edge have those AMT ribbon tweeters, which are very fast responding. If you feel that the Denon is too harsh/bright, you could try the Marantz SR8012 receiver. I really like the Marantz because they are the only receiver that has fully discrete analog stages. That being said, it does have the standard Marantz "warm" sound. Marantz has great dynamics, slam and impact. But the highs are definitely rolled off and softened. This might be a good thing if you want to tame those fast responding Martin Logan Edge.
One thing you could do is call Crutchfield and tell them you want to try these two receivers (Anthem MRX1120 and Marantz SR8012), but are unsure about which one you would like the best. They do have a 30 day return policy, so just return the one you don't like.
Just a suggestion. Every brand (denon, sony, onkyo, integra, etc.) will all have their fans.