Haven't really touched any of those boards, but it's highly doubtful all of those Caps are each actually shorted. They are all most likely on the same rail in there, so all are in parallel, and only 1 of them, or anything else that is also on that same rail, has the actual short.
See what the voltage on that rails is supposed to be, then inject that voltage and find the component(s) that is heating up first.