Do you have a reference for this? I assume the lower border is supposed to curve, like some kind of "poncho" like wrapper?
Generally, I would avoid having a regular pattern in that area if possible. Just think about how you would have to go about printing/planning this in real life, where my guess is that this would probably actually be designed and printed on a curved piece of material, but would still need some shrinking even then. There are brushes to paint along curves both in 2D and 3D painting solutions, but it might still be a pain. You could also try a cloth approach, but that's probably not worth the time.
In 3D, I would build a SubD mesh that has loops already shaped correctly along the borders and main directions of the pattern that are supposed to be parallel in the UVs. You can also start with your current mesh, remove a couple of loops and move it around while binding it to the surface with some kind of retopo tool. That way, you see the resulting distortion of the texture directly and can find the best compromise.
So to summarize: It's the mesh that's your problem, here, less so the UVs.
Keep the straightened UVs. With such a simple design, use the texture shown on the model as a template to follow, as you model the pattern with primitives. Set appropriate colors to the primitives to function as masks, and bake to texture. It'll look skewed on the UVs, but great on the model. If you decimate the model further after baking, you'll re-introduce the skew. In that case, just re-bake to texture.
That's a great idea, assuming the pattern is locked in, and you'd probably have to bake anyway if the end product is a lowpoly mesh.
And just in case: You'd only need to build a quarter of the wrapper, at least for the beginning, as it's a symmetrical shape, although you are more limited regarding the number of repeating elements that way.
In case you go the texture route, you could separate the UVs for each repeating horizontal pattern band for ease of adjustment.
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Generally, I would avoid having a regular pattern in that area if possible. Just think about how you would have to go about printing/planning this in real life, where my guess is that this would probably actually be designed and printed on a curved piece of material, but would still need some shrinking even then. There are brushes to paint along curves both in 2D and 3D painting solutions, but it might still be a pain. You could also try a cloth approach, but that's probably not worth the time.
In 3D, I would build a SubD mesh that has loops already shaped correctly along the borders and main directions of the pattern that are supposed to be parallel in the UVs. You can also start with your current mesh, remove a couple of loops and move it around while binding it to the surface with some kind of retopo tool. That way, you see the resulting distortion of the texture directly and can find the best compromise.
So to summarize: It's the mesh that's your problem, here, less so the UVs.
With such a simple design, use the texture shown on the model as a template to follow, as you model the pattern with primitives.
Set appropriate colors to the primitives to function as masks, and bake to texture. It'll look skewed on the UVs, but great on the model.
If you decimate the model further after baking, you'll re-introduce the skew. In that case, just re-bake to texture.
And just in case: You'd only need to build a quarter of the wrapper, at least for the beginning, as it's a symmetrical shape, although you are more limited regarding the number of repeating elements that way.
In case you go the texture route, you could separate the UVs for each repeating horizontal pattern band for ease of adjustment.