You don't build an accuracy rifle based on a pencil-profile barrel. Check this out - alot of the commenters in this video think that this means that barrel whip like this is okay for an accuracy barrel, but they be confused. Big time...
Hunting? Cold bore shot is the most important? Yeah, I get it. Building an accurate gun, for distance, from a pencil barrel? Foolish.
Since that's the goal, you need to research, and think hard about that pencil profile 20" barrel. I'm not dogging Faxon in the least, and never would - their 16" midlength 5.56 pencil barrel is the very heart of my own lightweight 5.56 build - and it's a great barrel. It's not for longer distance, though.
If 800 yards is really your goal, then you need to make the choice of whether you want some super-lightweight gun, or if you want an accurate gun at 800 yards. It's kinds like the Machinist's Rules - you get options, but you need to pick what options you want. Pencil-profile barrels and 800 yards aren't really one of those things that are gonna go together, unless you wanna drop a major amount of coin to a custom barrel maker - and most of those guys will tell you that they won't build it for you, no matter what you wanna pay them - because they have an accuracy or MOA guarantee.
You're trying to buy a new pet sloth, and train it to race greyhounds.
Here's what I was talking about, with Machinist's: