Welcome to the modern Rockwood world!
I put my mat in the storage area in the entertainment slide. I roll or fold it and slide it into a small bucket I carry so if it's wet, it drains into the bucket. In the same area I keep my chocks, 2 packs of leveling blocks, a set of leveling block caps, my spider electronic level and my entry mat and my 50' roll-up hose. that space is bigger than you think and it goes up, so think vertically.
I don't have your chairs, but all my other stuff goes under the bed through the outside hatch. It too has more volume than you'd think. My tools stay in the van, along with bicycles, food, clothes, firewood & misc. "stuff". It took me two week-end campouts to figure it out, but it works!
SF Bay Area
'99 Ford E350 V10
'16 Rockwood 8329SS