NOLACLS
Good thought on the flow through the container. I forgot you have a few extra drains in the overflows.
I have seen where people connect, or "T", several drain bulkheads together to make less piping. What I have noticed, and it makes sense, is that when they connect the two drains into one pipe, they increase the size of the pipe substantially to handle the flow. If you dont increase the pipe size, you are restricting yourself to the flow you would get from only one bulkhead and that pretty much defeats the purpose.
Is the input bulkhead to the skimmer bigger than your drain bulkhead? If not, I dont think you would have any benefit in connecting two drains like you were saying. If you have extra drains, it may not hurt either.