Those Diagonal seams are special stitching that are intended to keep the sail both taunt and resistant to tearing when stressed from varied directions at one time. Great for making a ultra lightweight material suitable for holding wind....not so much for allowing you to cover it with a paint without the diagonal lines popping out. And they will "pop out" because there is no way to cover them with either a dark enough or thick enough coating that they would still not be visible when a bright image is up on the screen.
In order for any coating to do it's work, it must be applied at a minimal thickness. With the material as described, that would entail applying a coating that just barely covers the existing color (what is that, BTW? ) The problem being that with such thin material (...and such material is extremely thin...) the tendency to "crinkle" introduces a worst case example of potential flaking and peeling. That might be reduced somewhat by only using a special adhesive primer such as Glidden "Gripper", applied as 3-4 dusters. I would not venture to state than any thicker emulsive-like paint...even dusted on, would tend to wear very well.
I know "Free" comes pretty cheaply, but it can also cost you a bundle in wasted effort, reduced viewing quality, and the dreaded "sour grapes factor" where you say, "I really didn't expect much for nuthin' nohow...)
So your left with this;
If you spray on the "Gripper" as 3-4 Dusters..... you must do so on both sides because the material is pretty translucent (usually) and the necessarily thin surface coating is not gonna keep light from penetrating through otherwise. A lot of light...and that means a net loss of light you'll need to illuminate sich a large surface area. Afterward...., both rolling and storage will have to be an exercise in careful handling and storage...and storage isn't gonna be all that easy with such a longish tube/roll of what will be material that has a delicate surface.
What you really need to try to wrap yourself around is the necessity of getting / using something that will work without paint, or in the least accept a paint in a more "user friendly manner". Like the plasticized side of outsized Black Out Cloth material....or Billboard Vinyl.
Of course, and if your willing to risk it, by all means go ahead and try the "Gripper" on the Sail Cloth, and treat it as gingerly as possible. It migh suffice...or it might even excel. Either way...win or lose, it will be a learning experience, and who can say absolutely if it will or will not work. I cannot...I can only speculate through assumption based on prior knowledge....a bit of actual experience, and the abiding desire to encourage people to "Do it Right the First Time"....not just take a "Stab at it".
Then again, people have been taking a stab at things on DIY Screens for as long as I've been involved on this Forum.
I know. I have the scars to prove it.