Hey Jeremiah,
Don't know if you tried this or not, but it's worked for me on occasions when I got a 2wd open diff vehicle stuck before.... ;)
Try applying the parking brake at the same time you are giving it some gas... Yes, this works... What happens is it slows down the spinning wheel, allowing the other wheel to get some power to it and if it does happen to have better traction than the other wheel, which is likely the case, because the wheel with LESS traction will always spin first, you might just have enough traction to get some forward momentum and get free..
I've used this to get me out of an empty farmers field I found myself in one time during my youth! Took my old 1971 Ford LTD for some off road fun! Well, got stuck trying to leave out another gate on the other side of the field!! Buried that sucker deep too..
Applied the parking brake and eased it out of there! No witnesses either!!
Except I had one dirty car and my Dad asking why I was washing my car at 8am on a Sunday morning!! The mud trail was a give a way regardless and all my Dad said was "did you get caught?".. "No"... He just turned around and left and said, "I don't want to know anything!"...
Good luck and yes, you'll have to take the abuse like a Man, but it will make for fun times and stories around the campfire! :)
Mitch