Once the pink is gone, it's jerky to me. I don't care for well done meat so I would recommend using a tenderizer. I have had tough elk before-typically when I didn't have time to age properly. Running through a tenderizer or learning the method with a sharp knife works. Essentially you are making a bunch of tiny slices half way through the meat from both sides of the steak. Be careful when you grill as it tends to cook faster. It's not a cure all but it makes very tough meat edible.
Another thought, you can ground the steaks without adding fat- then you can still grill to medium rare. Again, cooking time will be a bit different. One thing that helps this is to kneed the burger for at least 1 minute to activate the proteins. Pat steaks out to normal steak thickness. It will really sick together and cook closer to whole steak times.
Hope this helps.