Whereas I am not sure I can recommend the following, I am going to relay what we resorted to with Ollie. He too, ate everything out and about and also had a ferocious guarding response when he happened upon something he wanted to consume, to the extent it was impossible to either lure him away or get anywhere near him to remove him from what could potentially be very dangerous (in Glasgow we have unfortunately had episodes of dog poisoning in parks earlier this year, with meat being laced. 3 dogs died in April in parks we go to with him)
We decided to reinforce a 'leave' response but by laying down food that was deliberately awful tasting. So we coated bread in lemon, and the hottest sauces and one of us would go further ahead on a walk and put it down for Ollie to find. When he found it with the other person, they would say 'leave it Ollie', and 'Be careful' in forceful voices, and of course Ollie would leave the bread, as he could smell it was absolutely foul to him, and then we would reward him with a treat when he came to us instead. We did this enough times that he started paying attention to the 'leave it' command, because it made sense to him to - we were giving him good advice, rather than advice which he didn't want to hear because 'leave it' was usually paired with something that was very desirable to him and tasty. He began being able to generalise to other things that he wanted to eat because he started trusting our advice on the instruction. Of course we always picked up the bread afterwards so no other animals could consume it,
So that's what we resorted to because of the deaths of dogs in parks we visited and because his guarding response was simply unmanageable a few months ago. Like I say I can't say I recommend this as I don't want to be in a position of promoting other dogs feeling ill if they still did eat the hot sauce bread but we felt we needed to do something serious to manage our situation.