My personal advice would be to try and get Chester used to not having his food around all day, leave it down for a little while, if he's a picky eater, but after a maximum of half an hour, I would honestly remove it until the next meal time. It could be he does end up going hungry for a little while but he will eventually learn the new routine and I can guarantee you, he won't die of starvation! I would also still feed them separately but at least you know who's eating what and it'll prevent any potential fights over food in the long run.
My first dog was a dreadful eater and I used to have food down all the time but in the end, I made a rod for my own back and I swore I'd never do it again. I wouldn't have ever allowed my children to mess about with food, -" eat it or leave it but once you've got down from the table, there's nothing til teatime! ", so why should the dog be favoured any differently?
I've never had two dog simultaneously, so might be talking through my hat but I would imagine that having a set routine and set rules will help them both adapt.
Best of luck!