There's a couple reasons game (or any meat) might turn out dry. In my experience it has more to do with the handling than anything else, which includes if it's frozen, how long it's been frozen, etc. not just how you cook it, or any adjuncts you might use - though cooking any
burger beyond medium is going to dry it out. Adding fat can add moisture, or just make your burger greasy. Adding moistened bread crumbs is going to give you a meatloaf/meatball texture, not necessarily moisture. I have seen a burger recipe that insists on soaking the meat in cold water first, which is contrary to practices I have found for getting a good texture/flavor. Might work for you, but I haven't tried it, nor am I advocating it.
I also don't think much more than salt and pepper is necessary. If you want to taste the elk, then taste the elk, not bbq sauce, or seasoned salt, or whatever. But, if salt and pepper isn't good enough, then I suggest you seek this out, or look at the ingredients and make your own:http://www.thespicehouse.com/spices/bac ... tchers-rub