My Cookie is an alpha but does not have a thing for toys. She is just the motherly type.
Then, I have a foster, Sunny D, who believes that every toy in this house belongs to him. He is not an alpha at all. He is horrible about toys and does just what Eddie does. I pretty much do what you do, Mike. I have found it impossible to stop him and honestly I had other things with him that needed my attention. He used to be so high strung about food and would bite when taking treats out of hands. I have finally gotten him pretty ok with it but he still needs a reminder. The other pups in my home do not like Sunny and I totally get why. They do manage to keep toys away from him....but, often times he wins. I do what you do...just hand another toy to the one who got the toy snatched away. When they get fed up with him, they snip at him and he goes away for a bit. So...they do work it out. Is it the way I want it? NO.....I want them to share...but as you said they are not humans and it is hard to reason with them in such a manner.
I believe if they are not harming each other, it is best to let them work things out. When they get nasty with each other, I step in. I just don't get involved in little squabbles. I have 8 yorkies plus my fosters (sounds insane, I know

)and I have to say that I am very proud of the way they act together...and with new pups that come in. Friends of mine came over last night and brought their two pups...not an ounce of a problem. Guess you could say I am not much of a trainer....I really do stink at that...but, I do know (I think) how to help them live together well.