Multiple power supplies/sources for LEDs, how/where to ground with data line
Maybe neither.

If your distribution boxes are decent quality and have low internal resistance then you already have the common lines connected at the Lunch Box / Power Strip. Since this is the case all that is required is that you bring the power and ground of your sixth strip from the left back to distribution box 1. This will maintain your sensible arrangement of feeding all pairs of strips from both ends. It will also avoid problems and confusion should you lose power to one of the distribution boxes. If, for example, you lost the DC into distribution box 1 then the common connection for everything on that side of the system would be through strips 6 and 5 which may burn up.