Your 30-06 will be fine, easily the most popular hunting cartridge in my home state of Wyoming. Many non-residents go home without firing a single shot during elk season. Takes much gear and a pack mule/horse to get way back where the herds are hardly hunted.
You should consider hiring a hunting guide.
There are many game ranches that offer elk and red stag hunts for far less than a fully outfitted Rocky Mt packtrip. Some offer late season cow elk hunts for less than $1,000. Good meat and fun for affordable price.