It sounds like you have tried just about everything. 15 months is a really hard time to get through, I don't care what they say. Our son would do the very same thing, and to your acknowledgement, you have tried just about everything. The reason 15 months to 2 years can be so tough with a precocious little boy (he is smart and thus bored.) is because he is too young for time out or any other method of discipline.
He is so smart that he realizes the whole agenda about placing one or two items before him, so he says "ok, watch this." That is why all your efforts have been thwarted. All I can say, is do the best you can. Don't feel like a bad mother, because you take him out and see other little "angels" behaving and even worse get stares from their parents like "Wow, she must be really off base. Why can't she just control her kid."
I know because I went through the EXACT same thing. This is about temperment, attention span, and intelligence. Don't compare or let others compare your child to another. It is a complete waste, because all children are different.
I think that the only methods you can really do to even help is make sure he is hungry when you put him down and don't expect him to eat everything. At this age, it is good if you can get him to eat one good meal a day. They are experimenting heavily at this age, and they don't want to sit still to do anything. Of course, there is the idea to limit what is on the tray. Tell him no when he does it, and try not to give him too much attention for it. I realize you have tried all this already. Just hang in there, and consider purchasing a handy vacuum or a floor mat for easy clean up til things tame down a little. This is just a phase, or at least until he reaches an age you can discipline him and he can reason.
Believe it or not, you will like these qualities when he is older. He has an independent mind and he is not easily coaxed. LOL!
It reminds me of when my son was little and he would throw his toys everywhere. One of my husband's aunts told me she made clean up a game with her daughters when they were around that age. She was appalled by my son's behavior. All I could think was, um....this won't work. I gave it a try anyway, but it was all in vain. He knew exactly what I was trying to do, manipulate him into picking up his toys. So, he just ignored me. Later when he was older, I would take things from him or discipline him in order to pick them up, but this was much later.