My 8 month old dog growls when you go near his food. How should I deal with this?

Zeke is an 8 month old un-altered GSD from working lines. We've had him since he was seven weeks old. He is obedience trained and minds well. However, although I've had GSD's before, he is by far the most stubborn of them. In any event, he understands that he is "low man on the totem pole" and will accept corrections from any family member, although I seem to have more influence with him. One problem we cannot solve, however: Zeke hates having anyone within 3-4 feet of him when he is eating. He is crate trained, and his food bowl is next to, but not in, his crate. If he is touched or approached closely while he is eating, he will stop eating, "freeze," look very uncomfortable, and growl. When he does this to me, he acts as though he knows he shouldn't do this, but just can't help himself. He will let me touch him, and even take his food away, and not show teeth, but he will growl nonetheless. When my son (age 13) approaches Zeke when he is eating, Zeke will occasionally snap at him.

We have tried fairly severe corrections, and taking away his food, which he will tolerate. As soon as we correct him, Zeke acts very contrite, wagging tail, flattened ears, etc. However, the problem with him growling while eating (or even snapping) doesn't seem to be getting any better. Mind you, this is a dog who will do a down-stay, and you can put a treat right in front of him, say "leave it" and he won't touch the treat until given permission.

Do you have a suggestion? Should we be removing his food and NOT giving it back within a few minutes? What do you recommend? Should we neuter him at this point? He does not show aggression toward family members under any other circumstances, and he accepts strangers well, although he is very quick to bark if he hears someone approaching our door.

Thanks for any advice you can offer,
Andrea