But as for Dead-eyes, I think you might be going though a glitch. It's been a while since I've done that quest, so I don't recall, but if you've finished what the quest asked of you, then you should be able to pass (just follow the quest helper).
If you still can't pass, then perhaps One Eyed Jack could help you out better than I can... may even need him to reset your quest for you a little ways...
Wait...
There's no screen popping up saying you need to pay crowns to enter, is there..? If so, then that's a whole other problem...