Well actually, you have it pretty much wrong.
Look at the illustration on the left. In the center you see a 4' x 8' sheet. That sheet is overlaying the three sections, binding them together. Each sheet cost $12.00. Using the Trimmings you make all the side inserts. They don't need to stretch the entire perimeter....but they should overlap all the sectional joints by as much as possible.
And absolutely....if you can make a decision to just spend for another 5' x 10' sheet of something, then there you have your answer.
Not too terribly far from where you live, in Denver there is a company called :
Denver-Littleton, CO 80120
...................and there they sell Sintra / Komotex in 5' x 10' x 6mm sheets for between $96.00 and $110.00.
6mm won't roll up....but it will bend. And Piedmont can cut it down for you to the size you want. (60" x 107")
At 6mm, all you'd need to do is either hang it with adhesive directly onto the wall (...use a Silicone Adhesive Caulk and it can be pulled down if ever it needs to be...)
...............or build a Frame from the 1x5 as earlier suggested and hang it via the French Cleat method.
Unfortunately, unless you paint onto a wall, there is no your escaping spending some money. DIY can be inexpensive....even downright cheap. But free? No. I know you realize that...and we all feel the same way about saving all we can. But when your trying to create a large screen, there certain things to be considered mandatory. Your time with Do-able has basically spoiled you rotten as to the "Hang and Shoot" syndrome.
And don't you already know full well how so many others have not had that opportunity given Do-Able's limited distribution.
The Backer Board as illustrated was made so that two 1/8" thick layers of MDF Hardboard could be sectional-ized and assembled into one reasonable lightweight and rigid sheet to support flimsy material such as 3mm laminates, 3mm plastic sheeting, even 1/8" acrylic Mirrors. 1/2" MDF Boards at 5' x 10' can be had...but they too cost more than a little chump change, and are TERRIBLY heavy.
Sintra then is your best bet...not because it's free or even cheap, but because it's readily available, sized as you want it to be, and will be easier by a mile to work with. Why....you could even just use it for the Screen itself of your will ing to paint a high performance coating onto it, and then you'd realize a screen surface that would be almost an order pf magnitude better than any "Hang and Shoot" option out there.
Lastly, you could get Sintra in it's 3 mm version (cheaper by half - ) and laminate the Parkland to it. Then you'd have 1/4" thick material. But it would still need support to be able to "hang". Unless....., you cut back on the size of your screen just enough to allow for a 2" wide area outside the Screen area that would allow you to screw the Sintra / Parkland combo tp the wall with screws set into the 2" border area. Trim is then applied over that area to cover the Screws.