I don't own a 7mm-08 and have never fired one but after reading the reports here and looking at the ballistics I wouldn't have a problem if I needed to use one. It's would not be my first choice but I already have other options to go to and I undrstand needing to use what what you already have, and in this case you have a pretty good one.
I have a .243 my daughter used as the legal minimum but I found that to be a bit lacking. With the 7 you have a lot more bullet weight and choices to better suit it for elk hunting.
Good luck with your hunt I'm sure yuo will do fine.