So value is intrinsic if it meets some vague criteria of stability? How stable does the value of something need to be for it to be intrinsic?

Can you enumerate these "reasonable assumptions"? The idea sounds pretty dubious to me.

And yes, I would say that if the sun exploded, killing all Earth life, nothing would have value, at least not from a human's perspective. This doesn't seem to help the case for intrinsic value.

Sounds like a game of semantics to me. Value is a human concept, so eliminating all of humanity doesn't prove anything with regard to the nature of value, intrinsic or otherwise. That's like saying "poison is not inherently dangerous because without life on earth it ceases to pose a threat". Ok, that's technically true, but you're not saying anything meaningful since nothing has meaning outside of the human context. The point of labeling a quality as intrinsic is to point out that the quality being described arises from the fundamental nature of the thing regardless of how it is perceived. Food has inherent nutritional value because nutrition is a function of an object's physical composition. Nutrition has inherent value because nutrition is necessary for survival. The ability to survive has inherent value because it is a fundamental need of all living things.

I agree that food is pretty darn close to having a constant, stable value to all humans.

However, the edge cases aren't imaginary, and they give us a chance to refine our ideas.

Say there is a huge harvest and a town now has much more food than it can eat. A food merchant passes through the town and wants to sell some of his goods, however obviously no one is interested. Has the merchant's food lost its intrinsic value? Why doesn't anyone want it?

We can also consider the vastly different food preferences found all over the world. And so on...

Being a bit pedantic, food isn't really a specific thing, it's an amorphous category. It's literally defined as "anything people eat that provides nutrition", so it almost feels tautological to say that food has intrinsic value.

Finally, almost any other concrete, specific example I can think is much less universal than "food".