What do you feed him? Is there any way you can give him his food only when you're not there?

For instance, if he's on wet food you could fill kongs/hollow bones with his ration and freeze it and give it to him before you go out. If he isn't hungry when you leave, he will probably not be bothered about treats - whereas if your leaving signals "dinner time" then he might view it as a good thing rather than bad.

If he's on dry food, then soak it to much, then fill and freeze the kong/hollow bones like you would with wet food.

Food doesn't have to come in bowls

Leaving the radio on won't necessarily soothe him in itself; it's only if he associates the sound of the radio with being relaxed that it helps. If he associates the sound of the radio with you going out and him being stressed, then you might as well not bother