We did the 'trade' thing when zoey was a puppy. If she tried to do something we didn't like, we would redirect her with an appropriate toy, and itworked really well. I think it is important to have lots of dog toys around for this reason.
Have you trained him with 'leave it' and 'take it'? Not just leave it, but the 'take it' is equally as important. I don't know if we are just lucky with zoey, but she never really eats anything without our ok, and I think a big part of that is because of the 'take it' command. If I put something on the floor and she goes for it without me saying 'take it', I will remove it, so she has learned to only go for things that I say 'take it' for or else she doesn't get anything. So she won't put anything in her mouth unless she knows it belongs to her (ie, a nylabone) or we say 'take it'. This even works when I put steak on the floor, which is probably her best trick
We usually leave her in the bedroom while we are gone (there is nothing on the floor but this is mostly because she feels safest there since it is our 'den'). But thankfully, even when we let her roam alone she hasn't eaten anything she wasn't supposed to....So far at least. Knock on wood.
