I was about to agree with watermonkey but looking at the photos it looks like they changed the table. I have a campsite counter too but it's a few years old, doesn't have the diagonal cuts on the top at the corners. It fits into my 66" frame perfectly, if anything it rests on the two crossbars primarily and I'm not sure how much it sits on the siderails if memory serves. (mine is still on the trailer in winter storage too so I can't take a look.) I might have missed it if you said how wide your frame is, it almost looks like if it was another inch wide it would fit.
I run my straps over the top of the table and down through the holes, then under the rails and back over the top of the table (if that makes sense). That way I can just loosen the straps without undoing them to get into the drop bag and the straps just stay on the table when I take it off. I get a good pull on the straps that way and it's solid, plus then the passengers on the table can grab the strap for a handle. I think I use two 6'ers, one on each end.