I’m also printing on CRP with an R2880. I’m using Pro inks. I’ll give you my recipe to minimise these problems.
I gently brush the surface of the paper with a Kinetronics StaticWisk Anti-Static Cleaning Brush (model SW-140). I then use a Datavac Electronic Duster to blast the paper surface with high pressure air, and then also use it to blast the printer - the paper feed slots, the carriage bay and the outlet slot. Both these items can be purchased from B&H.
My hunch is that there’s loose paper dust sitting inside the printer, and that’s the cause of most of your problems. It would explain why the problem is printer specific. Which slot are you feeding from? You may get less dust generated if you use the rear feed, which is what you’d normally use for a paper that thick. The violence of the sheet feeder could well contribute to dust generation.
With most inkjet papers, there’s a very slight curve and the coated side is the concave side. With CRP, the coated side is very smooth to the touch, and the back is coarser. If you happen to print on the reverse (everyone does it once sooner or later), with CRP it’s usually pretty obvious, as the image is unsharp and flat, i.e. lacking contrast because the blacks are weak.