I don't understand the logic of NRS' "stock" setup with the 8" space between the foot bar and the cooler. Wasted space there. Yank the bar behind the cooler and shove the foot bar forward. If your cooler is wide enough (which it looks to be), you can use the foot bar to carry the back side of the cooler.
Run your lower straps from the bottom bends of the foot bar, under the cooler and up to the front bar.
Run your upper straps from the upper bends of the foot bar, over the cooler, and to the front bar. Loop straps work great here if you don't already have them. If the upper bends on the foot bar are too wide and the straps slip off the top of the cooler, swap sides so the left cooler strap is attached to the front bar to the right of the right cooler strap. Makes an inverted 'V' from the rower's perspective.
The balls of your feet can sit right above the bar with your toes against the cooler.
A combo foot bar does make this rigging easier.
Move everything forward 8" and you should have room to open the drybox behind your seat. You should also have room for a drop bag between the front drybox bar and your seat bar.
or x4 on the flip seat suggestion.