I have owned two E-350s, both 2wd. With all the weight in the front, especially the heavy 7.3 Diesel (which one of mine had) you have zilch traction on the powered wheels. You can get stuck in a low spot on wet grass, been there, done that. Tires help, and I ran BFG All Terrains which helped but did not solve traction issues. A heavily loaded rear axle would help too, but will also cause that axle to sink in sand or mud. My advice, learned from experience, is do not get off the gravel with 2wd E-350.
U-1300L Unimog with 10' Alaskan camper, OM-366A turbo-Diesel, fast axles, overdrive, Werner 12k winch
Various other mogs for work and play.