Could a bad radiator be causing all of this?

I know you said the test for a blown head gasket is negative, but I cannot imagine anything else that could cause that. Well, maybe a cracked block, but the gasket is much more common.

At that age, I'm pretty sure that either cause would cost more to fix than a much newer car. It's sad, but sooner or later, it happens to every car.

You're probably right.