First of all, objectively speaking, based on my spreadsheet that compares more than 60 AVRs, based on power output performance derived from soundandvision.com, the Onkyo TX-SR805 ranks top of
my list!!
None of the AVRs on your list would even come close, so if you need more power than you have now, be prepared to add an external power amp rated for at least 200 WPC 8 ohms or 350 WPC 4 ohms.
Now on the topic of REW:
Going by hearsay (reviews, forum talks) and some charts posted on forums, it would appear that Dirac>Anthem ARC>Audyssey XT32. Going by my own experience, XT32 can do an excellent job, with the flattest graph I have ever found on the internet after some tweaking with the help of REW (free software, highly regardes on various AV forums). The tweaking simply involved trying different crossover points, and use the Editor App, a $20 option, shouldn't take more than a couple of hours altogether. If you don't want to learn how to use REQ, you can just go by ears and pick the best crossover points for the main channels, or set them all to 80 Hz and the results should be practically as good as that obtainable by using Dirac Live. You can also try the L,R byapss option, so Audyssey can only affect the Subwoofer's response.
Experts like Dr. Floyd Toole,
@gene on this forum, indicated that there isn't much point to EQ frequency above 200-300 Hz, Anthem's default setting was 5000 Hz for their older MRX series (not sure if that changed for the latest models). Since I use REW (my seeing ears),and the Audyssey Editor App, I have control over the cutoff frequency point in order to get the best looking FR graph from my main mic position.
So based on the above, my opinion is that Audyssey XT32 + Editor App+ REW with UMik-1 mic ($75) will get you the best bang for the $.
One last point, some people claim that Room EQ is not good because it will improve you main mic position while messing up your other listening/sitting positions. That got me curious at one point so recently I spent some time using REW to measure the response at my other possible listening positions and found such claims to be incorrect, at least to the point I can say confidently that there is no need to lose sleep over such claims.
Now, let's look at your listed choices:
Marantz SR8012 - The Denon AVR-X4400H + Audyssey Editor App, for $920 is actually the best deal right now, obviously it is not the same as the SR8012, but I have to tell you that I just replaced my Marantz AV8801 (paid well over $3,000 only 5 years ago) with the Denon and am very happy with my decision. Having just experienced this downgrade (price wise),or upgrade (feature/performance wise),I am almost certain that I will NOT ever go back to separates or flag ship AVRs. It is just too much of an investment for something that one will not likely keep for longer than 5 years.
Anthem MRX720 - If you are sure you won't need more than 7 channels, and the latest features that are not available on this unit, then it can be a good choice if you can get one on clearance for under $1,000 brand new. Even then, I cannot think of one single reason that it could be better than the cheaper AVR-X4400H, or SR7012, or even the SR6012 that is half a notch below. Anthem ARC is good, but I have not seen a better posted plot than my own XT32 plots even if we ignore the frequencies above 200 Hz.
NAD T777 - Nice modular concept, and Dirac Live is a plus, but you will end up paying much more for less overall, in terms of power output (based on past bench test data) and features. Note that NAD has excellent IFH dynamic ratings, but those ratings are based on IHF standard, that is for a very short duration. NAD literatures might not have mentioned the test duration and/or their method of tests, but if they went by IHF for dynamic rating, it wouldn't be longer than a 200 ms tone burst. Using the same kind of tone burst tests, most D&M AVRs in the same price range probably can perform just as well. A $899 AVR-4400H used as prepro with external power amps $1,300 can certainly do much better and you will likely pay less and have more in the end.