Mike--when you say not cross each other, you mean physically, I assume? And thanks, everyone, for the advice. I'm going to star ground my outlets.
See what you think of this: I will have the electrician--helieve it or not, he's more than willing to do all this, unlike some other electricians I've talked to who think it's all nonsense--run a copper grounding rod into the earth. I'll run separate wires of equal length to the grounding rod from my outlets. Then I'll also ground the main breaker box, which is currently only grounded to the copper water pipe, with another wire running from the pipe to the grounding rod. I'm doing this because I've been told that everything should ultimately be tied to the same grounding rod? Does everyone agree?
Or should I just run the three outlets from the subpanel back to the grounding rod?