With no PPs in any state, about the only states I can think of that have OTC elk licenses for hunts on public land are ID and CO. You're probably not going to get away from crowds or meet any of the other requirements you mentioned anywhere out west any more on public land, especially if you've never even hunted elk before. You need to realize that what you're asking for is probably going to require spending a considerable amount of money to get a landowner tag and go on a semi-guided or guided hunt in a state that has those tags available. CO, UT, and NM are several states that I can think of right off the top of my head where I'd start looking.