Just putting my thoughts in at the last minute. I know you were looking at Emotiva stuff. I’m actually a pretty good fan of Emotiva amps. I started with an XPA-1 and now am running all XPR-1 and XPA-1L (for surrounds). Emotiva is a different model where there is no middle-man markup. There are better amps out there, but for what you are spending, Emotiva delivers a LOT and it is very difficult to find something equal without having to spend a whole lot more. Keep in mind that the Gen 3 is a different beast (it uses the XPR amp boards, but it also has a switching power supply). I have not heard the Gen 3 amps. You might try stretching your budget to get a couple XPA-1 monoblocks. They are on sale now for $1019 each. You do have a 30 day return policy on these. I get the feeling you like playing music very loud. On the XPA-1, you can also run them in Class A mode (which will help with midrange body and help reduce any brightness/harshness).
Getting a 600watt monoblock doesn’t mean you use all 600 watts. It means you have a huge power supply to ensure there is no drop in current or distortion in the signal. It also helps with strong bass response. The Rotel should sound clean because it will have more power supply current available since it’s not using the internal amplifier at all. I’m not sure that the Parasound Halo integrated would help much with your volumes levels, since the power supply is not really any larger. The Parasound will sound much better than the Rotel at lower volumes, but would not really be what you need for the louder volumes. In my system, I can get my B&W 805 bookshelves to really pound with my massive XPR-1 amps - they are only one 6.5" woofer in each speaker. The amp does make a difference.
A sub could also help, but there are challenges with using a sub as well.