I know it's a pain in the butt (no pun intended), but in training Malone we consistently got up EVERY morning around 2, and very gradually weaned him later and later until it was all night. It's not very fun to crawl out of your very warm bed to walk circles out in the freezing cold grass! But it served several purposes--he learned that he could hold it a few hours, and it also re-enforced the concept that he goes OUTSIDE. Now he sleeps thru the night, and when he REALLY has to go he wakes us up with his whining.

Is Zeke crate trained?? That helps a lot also because they don't want to "go" in their sleeping place. Hope this helps a little!