How do you get clean stripes on fringe textures without the colors muddying?

Did one of these fringe-covered lizards a while back and the answer is basically both of your options combined. Base the whole fringe area white first, yes, that part of your plan is right. But don't try to stripe across the whole flank in one go. Paint each paper strip individually, top to bottom, and treat each strip as its own tiny rainbow. It sounds slower but it's actually faster because you're never waiting for a whole row of bands to dry before touching the next color.

The bleeding happens because you're dragging wet color along the strip edge. Two fixes. First, use paint at almost full strength, maybe the tiniest touch of water, not thinned down. Thin paint wicks into the recess between layers and that's what causes the muddy pull. Second, work each color from the middle of the strip toward the edge rather than starting on the edge. You get a cleaner line and the paint doesn't creep under the lip of the layer below. A trick that saved me a lot of headaches: before any paint goes down, run a sharp pencil lightly along each strip and mark where the color bands change. Then you're filling in shapes instead of eyeballing it wet. Also do all the red bands on every strip first, then all the orange, and so on. Same color in the brush means you can move strip to strip without rinsing and without waiting, since you're coming back to a band that's two colors away from the last wet one. For the spine ridges, purple works fine if you keep it flat and unblended. The piñata look is all flat blocks of color anyway, so a solid purple ridge reads as part of the palette rather than clashing. I'd avoid doing a gradient on them, that's where it starts fighting the stripes. Maybe pick the deepest purple in your rainbow set so it ties to the fringe without stealing attention.

Last thing, do the recesses and gaps between the fringe layers last with a dark wash or just a dark grey thinned down. It separates the strips visually and hides the small slips, which honestly is half the battle.

Reading this made me feel better about my own attempt, mine ended up looking like a clown suit caught in the rain. One thing I noticed on mine was that the strips near the tail are skinnier than the ones near the head, so my lines kept getting sloppier the further back I went. Ended up just doing those last few with a solid pinkish color instead of proper stripes and honestly it looks fine from the table. Does anyone actualy notice the messy parts once the model is sitting on the game table a few feet away, or is that just me fooling myself?

Agree with doing each color across all the strips in one pass, that's what finally worked for me too. The one extra thing I'd add is that I kept smudging finished bands with the side of my hand while reaching across the model, so I started working from the tail end toward the head and bracing my wrist on a cork instead of the model itself. Also a cheap makeup brush is way better than any of my actual brushes for catching the little slips of paint that pool at the bottom edge of each strip, you can wick it off before it dries.

You mentioned the paint pulling on the edges. Since those paper strips are really porous, I found that the paint gets soaked into the fibers too fast before it can dry. I learned this when I was working with industrial coatings on a large structure. You need a sealant. I suggest using an acrylic gloss varnish, thinned fifty-fifty with water, as a base layer on the entire fringe section first. That locks the paper down and makes the individual color bands really pop. It totally stops the wet paint from sinking into the material and losing its clean line.

One thing I learned the hard way on a similar fringe-heavy piece is that the biggest enemy is consistency of the band order, not the edges, because if the rainbow runs red to violet on the left flank and violet to red on the right your brain notices somethig is wrong before you can name it. I made a little paper strip with the sequence written on it and taped it to my desk, which sounds absurd but saved me from repainting an entire side. Also, small slips in the bands are easy to rescue after everything dries, a steady hand with the base color over the bleed fixes most of them without redoing the strip.