You will find that any thirty cal bullet will tear up that hide as will a 22-250 if you are not careful, I hunt coyotes with 22-250s but will lay one down with my 308 if opportunity arises. If you are bound and determined to use a 308, I would stick to Speer 110 grain spire points or if you can get them Speer 100 grain round nose soft points.
My recipe for my 22-250 is as follows:
Rifle Remington 700 1:14 barrel and Winchester 70 with a 1:12 barrel : 34.0 grains of Varget powder in Winchester brass that has been trimmed to 1.902 and the flash hole trimmed out. The primers are either Federal or Winchester standard primers for above freezing temperatures or for below freezing I go to magnum primers.
I have been fortunate enough for both rifles to like the same recipe. That beening said the Winchester which is older it the go to gun for me.
I just noticed that you said that you have a crap load of military brass. Remember that you have to cut out the crimping ring that is holding the primer in and that military brass has a smaller capacity than civilian brass does, so you will get higher pressures with the printed recipes, so reduce them accordingly say by at least a half a grain to start and do not under load, that is to say load any less than the least amount of powder shown for a load and conversely overload your brass. We'd like to see you around for a good long time and healthy! Good hunting and God bless.