I currently have a tri-fold hard cover and also appreciate the third bed dry storage in front. I don't have any problem getting totes or boxes of firewood under there. However, I come in from the sides as I have a narrow hitch on rails. I can see it being a problem if you have puck mount as Ram designed those to sprawl all over the bed. In hind sight, I would have preferred a Backflip cover which is a hard cover that allows full bed access; probably what you are looking for.
Don't mean to be a wise -A, but it would be cheaper to replace the big chest with two smaller ones.