300 yard max gives lots of options. You don't need a 30-06, 6.5 Creedmoore, or an AR10 variant. Lots of AR15 calibers available and would leave you with more money for glass and a much lighter rifle. 6.5 Grendel, 6.8 SPC, and maybe 224 Valkyrie is where I would start. Even 300 blackout would work.
Personally, I'd go 308 instead of 30-06 if you are leaning that direction.

It is far more important to be able to hit the target than it is to haggle over who makes a weapon or who pulls a trigger.

� Dwight D. Eisenhower