When I first saw this "larger game" I thought you were going elk or moose hunting. But sheep and bou, those critters aren't exactly what I'd call big so I'd say just use what you use for deer where you live.
I know of more than a couple sheep and bou's taken with 22/250's and Swifts and 243's and the like. So, your lil 7 won't have any issues at all.
If I were taking a 7/08 I'd use a 139 Horn coupled with R17 and call it a day.
Are you hunting this fall?
Thx and best of luck to you (take lots of pics and come back and share)
Dober
