He sure tall!
I hope you find a solution for travel. When we traveled my friend made some...things...for the kids to sleep on on the hotel floor. She got a bunch of towels the same size, like at the end of summer when they have all the beach towels on sale, then sewed them together. She made a small pillow for each one. They were several inches thick too. When it was time to go we rolled them up like a bedroll and they went under the seats of her van.
They washed pretty easy since they were normal towels and they dried outside in one day. They were sort of too heavy to go in my dryer. It was an old gas one that took several hours for just a normal load.
That worked really well.
When I was traveling with the kids I bought the thicker Kindergarten nap mats and sewed a huge pillowcase like cover for them. I added an attached piece of fabric they could cover up with if they wanted to. It was pretty comfortable too. It folds flat and does not have to have the cover taken off to be put up.
There are many ideas for traveling out there for sure. BUT at home he's plenty old enough to start sleeping in a regular bed. It can be straight on the floor if needed for a while but the younger he's put on a bed the easier it is.
In my child care center we had a whole closet of camping cots. They are a wooden base with a canvas "bed" on them. They fold the opposite way and get really small, so small they are comfortable for military guys to carry on their backs.
Here's a link to a picture of one, it's on ebay but it's the same as the ones we used. The kids never got too tall for it since it was for an adult. It was also very comfortable. The 4th picture shows how it looks folded up.
http://www.ebay.com/itm/vtg-folding-wood-canvas-cot-hunti...
Here's a better version. It's light weight metal so no splinters and aluminium is lighter to carry than wood.
http://www.amazon.com/Rio-Adventure-Military-Style-Cot/dp...