I'd like to offer a little bit different perspective and I hope you'll take it as kindly as possible. A number of years ago I got a house in the country with a little bit of land and quickly bought some sheep as I had grown up raising them and thoroughly enjoyed having them. My next door neighbors had a dog that was very nice and I would never have minded her visiting. One day, however, that dog who I don't believe had ever hurt or chased any animals, got with a pack of other neighborhood dogs (who probably were also normally nice, gentle animals) and they attacked my sheep, killing one, maiming one to the point that I had to put her down and injuring another severely. My sheep were in my backyard that was fully fenced, but someone else's dogs were able to find a way in and kill and hurt my animals because their owners did not have them fenced in or tied up.
What I'm saying is YOU know your dog is never going to hurt anything. The neighbor knows that most dog owners will say the same thing. They have animals THEY want/have to protect and understandably will do so by any means necessary.
I'm sorry but none of us knows what will happen when our sweet, loving dog/animal gets into unfamiliar circumstances. You said that he will take eggs on the ground, but you think that's fair game - what if your neighbors don't? You said he digs but not much - what if your neighbors think any digging is too much? You said he's playful and likes wrestling with other dogs - maybe you neighbor doesn't like playful dogs or ones that might look aggressive because they're being playful.
Having a pet of any kind means taking responsibility for it and if we're unable to then that pet should go to a different home. You're looking for a new home for him which is commendable however I wanted to add a different perspective for your neighbors. Maybe they're crummy, maybe they're not, but I'd probably do the same thing they're doing if a dog kept coming in my yard after I'd made it clear they weren't welcome.