Is it possible for you to gate the kitchen off at all? I know you mentioned not wanting to stop access but I feel like this is a tough area because the only time to train this is when caught in the act/almost act and if he continues to be able to get the gratification of eating (even if you reprimand him), he's probably going to keep doing it. If I was able to gate the kitchen then I would probably ungate it at times where I could pretend to be going about my day, but actually watch and wait to step in and reprimand.
Does he take food off your lower tables such as coffee or end tables? Leaving food there and then training to that situation could be another idea though I don't know if he'll transfer it to the counters.
I also think someone has mentioned on here before anti-counter surfacing things you can buy that if your dog touches it it buzzes or something.