Hi Eric,
I have a Ruger M77 7mm-08 I bought new in 1982 for deer hunting in Utah. It has a 1:10 twist with a generously long throat. Quite a bit different than yours so keep that in mind. I've been working up loads with 6.5 StaBall and Varget, Alpha brass, Federal 210M primers, and a variety of bullets. You'll probably get more mileage with your modern barrel and action and certainly have more bullet options with your faster twist.
I hunt Colorado elk at altitude of 9000 to 11000 feet. I've killed several inside of 200 yds using 150 gr Nosler Partitions. But one hunt I did have to pass up a couple of 300 yd shots because I didn't think my load had enough oomph for that distance. I got a chrony and turns out I was correct. With that in mind, I wanted to work up a load that carries 1700 ft/lbs 300 yds down range at 9000 ft altitude.
Using my sentimental deer round Hornady 139 grs BTSP, I get around 2650 fps with 45.5 grs of Staball with a COAL of 2.83. 46 grs was too hot.
For copper I ended up in the Hammer world. The gun loves the 140 gr Absolute Hammer. With 41.9 gr of Varget, it routinely meets or exceeds my target velocity of 2755 fps with very good accuracy. 47 grs of StaBall was consistently faster around 2780 fps. Bolt lift was not heavy, but closer examination of the brass showed it was too hot. I'll back off to 46.7 grs. COAL is 2.825 which puts the neck even with the first power band on brass 2.025 in length. Distance to lands is not applicable with Absolute Hammers. Stability should be good down to 5100 ft with my 1:10 twist
Looks to love the 130 gr Absolute Hammer as well. I got 2900 fps with 43.5 grs of Varget. Going to work up to 44 grs of Varget to see if I can reach or exceed the target velocity of 2930. Going to try 47 grs of StaBall as well. COAL is 2.805. Stability should be good down to 900 ft altitude.
I like the 150 gr Stone Hammer which is strangely efficient. I get close to my target velocity of 2690 fps with decent accuracy using 44.5 grs of 6.5 Staball. COAL is 2.67 with a distance to lands of 0.05. Hammer bullets in general seem to be less sensitive to distance to lands but this one is a "blunter" bullet so you have to pay some attention.
I like the high BC 132 gr Hammer Hunter Tipped. I get close to the target velocity of 2835 with good grouping using 42.8 gr Varget and a COAL of 2.835. However, for me, it groups 5 inches to the right of the 140 gr AH at 200 yds.
The 136 gr Stone Hammer should be an excellent mid-range all altitude deer round. I get around 2750 fps with good accuracy using 45 gr Staball and a COAL of 2.77. I just don't hunt deer much anymore.
For me I'll probably settle on the 140 gr and 130 gr Absolute Hammers.