Can two different players have the same coordinates?
I think your existing script could be augmented to make sure the same coordinates aren't picked more than once. Just add unique ID values for your hidden fields and loop through the existing ones to make sure that it wasn't already added.
You could then do the add to cart all at once and do a secondary check as it is actually added.
This might be a good candidate for a premier support ticket. I should be able to help you with the necessary adjustments without much difficulty but it will certainly involve some hand coding both in the client javascript and php.