I actually got it out without doing any damage.
The area between the overdig around the house and the hill I was standing on to take the picture was only a little wider than the machine. Even though you can't really see it in the picture, it also had a slight slope toward the house. Needless to say, it was *really* greasy back there. My intent was to back in as far as I needed to, and use the hoe to pull dirt from the hillside and backfill the house with it, working my way out. Once I got back that far every move I made, either forward or backward, caused the front wheels to slide a little further toward the house.
To get it out I had to go get a skidloader. I cut a notch in the hillside opposite the front bucket long enough to back the skidder into. We chained the skidder to the front loader arm. I swung the hoe all the way to the side and chained it off to a decent sized tree. With a coordinated effort, the skidder pulled the front and the hoe pulled the back. It was greasy enough that it slid sideways right up out of the hole with no damage to either house or machine.
As far as being wiser and more experienced, Yeah, I'm more experienced--I know how to pull a 580 sideways out of a house foundation. Wiser, I don't know...