Sandra, Poor you!
I think soil analysis is the way to go with this - at least you'd have some idea of what the dog is after in the soil - be it nutrients or dead things. I think blocking access to the site is a priority - your vet is right to say that as long as things are moving along it's all Ok - but....eating lumps of dirt and stone aren't the best things to keep the digestive tract open and functioning!

Try adding a teaspoonful of vegetable oil - or even better - a capsule of cod liver oil to the food every second day. If you can get access to a swimming area for the dog use it - not open water in the winter, a swimming pool - but that excersise without impact is brill! Giving the dog time to stretch and warm up before excersise is useful, so a walk, increasing gradually in pace, is a good idea before free running. It is also useful to cool down after excersise. It may help joints and muscles relax and be less stiff.
Good luck and let us know if you get anyone to look at your soil - most interesting!