Labgrade. I don't use the 7-08 but I do use a 7x57 mauser which is pretty much the same thing ballistically. A load I like is the 154 gr. Hornady Interlock at 2500 FPS. Looking at Hornady's newest manual, you should be able to come close to that or even a bit better, even with your shorter barrel. They show a max load of H-414 giving 2700 FPS. Allowing for your shorter barrel, 2500 plus FPS should be attainable. They even show thw the 162 gr. BTSP reaching 2700 FPS.
I'm not too much of a fan of premium bullets. The one time I used some, they failed me miserably. I got the deer, but five shots, four of which would have be fatal almost instantly had I be using my regular deer load, rather than the elk load with a premium bullet. (Both my deer load and elk load use a 180 gr. bullet at 2700 FPS in a 30-06. I was out of deer loads and didn't have time to load any on the last day of the season.)
At the velocity the 7-08 and 7x57 are capable of reaching, it seems to me that a conventional bullet should be more than capable of bringing an elk down. I'm planning on using the 7x57 for both deer and elk this year. I'll use either a 139/140 gr. for deer and a 150/160 gr. for elk. I'm scheduled for some surgery in 5 days, and I will probably have to keep recoil on the light side this year.
Good luck on your hunt, and I hope your wife fills out her tag.