I've got a 6.5 grendel that I really like. I'd look into the grendel or 6.8 in the ar platform. The thing that made me go with the grendel was how cheap you can buy bulk ammo for. Ive found grendek bulk 100 grain steel case for under 25cents/round

The only reason to go with 300 blackout is if you plan on suppressing it or building an ar pistol/sbr

300 blk shines as a suppressed subsonic slinger in a short-barreled configuration. But that isn't the only reason to consider it. 300 blk shares everything but the barrel with your 5.56 if you already have one. Has around a 30% increase in energy over 5.56 at all barrel lengths. Has options, though pricey, that will expand down to very low velocities. Is very effective for killing at the most typical hunting ranges (50-150 yards).
I skipped over the 6.8 and went straight to the 6.5 Grendel for my longer range work. I would not hesitate to shoot a deer at 500 yards with my Grendel if presented the opportunity.

For a Lightweight, deer rig it’s hard to beat the 6.8 in an AR 15. It gets most of its performance in short barrels, and you can have an accurate, 300 yard deer AR that’s under 6#, or less, if you want. Nothing wrong with other calibers, but I’ve got all sorts and can/do build all sorts, and I carry and kill deer with a 6.8 usually. If I was worried about shooting beyond 300, I’d go straight to the 6.5CM AR, or a bolt gun. The longer bullets usable in the 6.5 are better suited than the constraints of the Grendel...to me. I just enjoy a short, light gun when getting in and out of vehicles and stands. I just don’t see any need for the non-standard AR10 for 95% of deer hunting. The Grendel can do it in a short, light package, also. It just isn’t quite as efficient in the shorter tubes, but it’s splitting hairs inside 300.