I'd rather do a full work up than "random" but your proposition of bullet/task shall be fine.I probly wont be driving these to god like speeds, just sub 2800 and for shots out to 300 yards on big deer.
You mention large deer. This is what I hunt. Whitetail on the Northern end of their range where they attain maximum size. A 200 lb. Animal is fairly common. I found the btsp at 308 speeds a bit soft at shorter range. The hot core and GS in a lighter weight about perfect.I probly wont be driving these to god like speeds, just sub 2800 and for shots out to 300 yard s on big deer.
Hornady 139 SST is my go to bullet in 7mm-08.
I've used the HotCors for years in several calibers. I was bummed out when they dropped the 120Gr HC in .264. Shot many deer with the 130 gr in a 270.Also heard good things about speer bullets, about to start loading them for lever guns.
My understanding is that you would want the Flat Base bullets as the Boat Tails are built to expand easier/less robust. I think I read that from speer somewhere.
Of course that may depend on your definition of "Big" deer
plus one for the Hornady 139 SSTHornady 139 SST is my go to bullet in 7mm-08.