I know a bit late but Two ways to get out of mud or snow.
Get some long strips of carpet , they work wonders.
Lastly one of the best tips I ever got while trying to get a stuck tractor out , was to fasten a log about 6" longer than the diameter of the main wheels to each side , used chains to tighten it up and it works like a paddle steamer ,
I am sure your wheels are wider than bodywork and a 2x4 chained /roped to wheels might have worked