You can use depron. Depron doesn't have a paper on it. You will have to do hot glue/tape hinges (google them) and for theA/B folds it will be a little tricky. Depron is super light, and fairly strong in the thicker variety.
You can get it 6mm 1000mm x 700mm (40 x 27.5"). 10 sheets for £25. More expensive than most stuff, but it is just as versatile of a building material.
Any more Q's I would be happy to answer, but I will tell you what doesn't work. If you are going to order any foamboard, you can check it first. Ask for a sample sheet. If they say no, get an A4 size (never more than £2 including shipping) and weigh it as accurately as possible. Scale it down to a square inch, and if it weighs more than 0.3g then it's no good.