300 Win Mag with 180 gr Nosler or 208 gr AMax is exactly the medicine you are looking for.

I own the other two you mentioned plus the 7 Rem Mag as well. The 270 is a factory Remington with a sporter barrel that shoots sub moa, but loses a bit of oomph quick after the 550/600 yard mark.

30/06 is a 2nd year production model 721 Remington. To say this is an superb specimen is an understatement. VERY nice rifle. Because it is a late 1940's rifle, it has a fast twist, so it's preference is 174/176/178/180 gr bullets. Would not hesitate on a deer at 800 yards.

The 7mm Rem Mag is a Savage that I built with a barrel bought from another user on this site. Yep, I would definitely feel confident shooting (and hitting) a deer at a grand with a 162 AMax.

The 300 win mag is a factory BTCS Savage. Single shot blue receiver with a blackened stainless barrel. Wears a 16x40 Leupold with turrets that is about near a marriage made in heaven as it can be. Ever want to show off shooting...this is a go to rifle. 180 Nosler or 208 gr Amax when going past the 900 yard mark.