Depending on tanks size and your set up you don't need both chambers of media.
The problem will be that the PS should be in a section of sump that never has fluctuations in water level as that will effect the skimmers performance.
I run my skimmer in last section of my sump but I waterbridge a 29g to my sump to diminish the effects of evap.
You could always get an ATO for the sump if fluctuations are really a problem.
the dividers/overflows are to control micro bubbles from re entering the tank.That may also be a problem with having the skimmer last in sump?