Answer: Oh, oh! Crown Vetch is wonderful stuff where it can be contained and where a thorough ground cover is neccesary. However, as you have found, it is VERY aggressive!
You are right. Using chemicals over your water source would be fool-hardy! Since you don't have anything growing there now, I'd cut back or pull out the remaining vetch and cover it again with plastic. Every few weeks, uncover it and pull out or cut back what you see again. This will be a tough "go", but perhaps the only thing possible without using chemicals. Hopefully, by the end of this growing season, you will have no vetch left.
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