Here's what I came up with: essentially it's a shed tote made of landscape timbers, bolted together in a square, with the back cross timber on top of the skid timbers, and the front cross timber below, which would angle the skids up allowing for it to be more easily dragged along.
And here it is:
The next pictures show the process of a move:
And the goats check out the "new" place!
Thanks to the Lord for this idea and for the resources to be able to put it together.