You've said the magic words of "Jojo" and "fabric choice" and have summoned me.
For those looking for reference images, and assuming you are doing the basic outfit because you didn't specify: https://s-media-cache-ak0.pinimg.com...er-bizarre.jpg
(I grabbed one that looked the least shiny)
Honestly, my Jojo cosplay philosophy is that the more obnoxious, the better, but I understand that tastes differ. Even so, Jolyne's outfit is usually rendered with at least a small amount of sheen to it, so while a super matte fabric would work, it wouldn't be my choice.
If you don't want to go shiny, I'd recommend using the backside of a shinier spandex. Not like a mystique dot where the shine is printed on, but where the shine is part of the fibers itself. The backside of raschel knit spandex ("regular" spandex), where the front side has some shine to it, would be nearly perfect. The backside of satin spandex would also work well.
I'm personally planning on using a mystique dot once I get around to default!Jolyne's shoepants (not doing this outfit, but she wears them with the handcuff shirt, which I am planning), but again, that might be too shiny for your tastes.
If the problem with the Ultrapreme is that the dye bleeds, it shouldn't be too much of an issue unless you are appliqueing on the stripes, but I'd be worried about the chest applique. Maybe buy a small amount, like 1/8 yard, and see if you can wash it a few times in synthrapol or a similar detergent to remove any excess dye before going for it for the whole thing.