The only problem I had with the 1yrd skip loader up my hill was at full capacity it had trouble with the traction so I had to undercut the yard amt and basically guessed how much to dump. Some of it, the bottom, was heavier than the stuff on the top. So if you can dry your soil even tho you're not really supposed to it may help.
Other ideas.
Remove all slick oak leaves. Have a fuck ton of sand on hand. See if the place will rent chains for the wheels.