BLUF, I'd recommend that you get the device replaced, because I think that if the battery is routinely running that hot, you have a problem. It may or may not be software, but the carrier has already agreed to replace it. Take them up on their offer, especially because the camera is scratched -- I've read that Sprint often tells its customers to pack sand when its refurbs are in worse shape than the devices they replaced.
I don't typically use QC/Fast Charge either. My bedside wireless charger is an older Qi charger with a 1A charge field. My phone charges slowly all night.
If you're consistently trying to get six hours of screen time, the phone is going to run hot, especially if the screen is on for long periods (long games, movies, etc). The screen is the biggest single power draw on the device. The S7 Edge has a liquid-filled cooling coil inside the case. When the device gets warm, that's the cooling coil discharging the heat that it's drawing from the components. Having said that, I think that the phone routinely running that warm would concern me too.
I'd drop the Lux brightness app. The auto brightness on the newer Samsungs is so much better than it used to be that I dumped it right after I got my S7E. I took it off of my family's other Samsungs too. That's a constantly-running app that doesn't need to be there. I'd leave Greenify off as well for now.
FWIW, I don't know of anyone with a S7E or any of the 2016 devices that can routinely get a lot more than four hours SOT on a charge with normal use. Yes, I'm sure that we all know of an exception. I know a battery extremist who can get a lot better, but it's after a lot of coddling and attention to the battery and every little thing on the device. But she's a slave to her phone -- she obsesses over every bit of power usage to the point that she doesn't just use and enjoy the phone.
My first recommendation was to replace the device. My other recommendation is that you take your new phone and set it up as a new device. Resist the temptation to restore from your Google or Samsung account. If your issue is an app or an app setting, you'll stand a very good chance of reloading your problem back onto the new phone. I would load the Gsam battery monitor. If you want to use PDP, be very careful and disable just the carrier bloat. Leave the Samsung and Google stuff for now. No more utility apps. Let the phone run as intended (including the various default measures like auto brightness with the base near 40% or so, power saver at 15%, etc) for a few weeks to make sure that the phone itself is good. I suggested a few weeks because you'll spend the first several days fiddling with the phone while you load apps and such. A few weeks is long enough that you get past all that and just use the phone.
If you're determined to get something from every mA of power expended from your battery, look at the advertised battery performance of the phone and realize that whatever that number is, it was developed in a lab in ideal conditions, not in real life. I doubt that you'll find that Samsung promised anything near six hours SOT. I don't know what phone is out there that will routinely give anyone six hours of display time on every charge.
Every time that you charge and discharge the battery, it's capacity will be reduced just a little bit more. Over time, the SOT WILL go down. Understand that the battery began to break down the moment it was built, and you can't do anything about it.
Your S7E is an awesome device with a lot of capabilities. I'd suggest that you just use it and see what happens without the worry. You can get a decent 10A power bank for less than $30 for extra assurance that your battery won't run down.