Neat vid! Pretty informative and detailed too. Good work!!
I'd suggest using a wax and grease remover, like PPG DX330, using white shop towels after the washing and sanding as well as after the masking. When the towels come up clean, you're done. Paper towels tend always to leave fibers behind. If all you have is paper towels, it's a good idea to use a tack cloth before paint. It's just what I would do, but I do realize there are many ways to skin a cat.
Little tip for the Mazda guys doing this to theirs, remove your door panels, mirrors, and rubber coated "elbow" molding below the window. It just un-snaps from the door. This makes everything easier to mask. But if yours are already peeling from the tin they're adhered to, which is common, peel it all off, prep, and paint with whatever paint your using for the "racoon eyes" aka Black around windows. It may still peel after you just painted over them.
'01 XLT disguised as a '03 Fx4 Level II
Big. Loud. Slow. Bright.