I want to transfer a seamless texture tile into a UV map

I’m working with DAZ’s Genesis1, which is already UV-mapped, with torso and limbs in separate sections. I want to give the model a scale texture, and I’ve made a seamless texture tile. So, the first thing, I’ve followed tutorials on taking a texture from one set of UVs and projecting it onto a different UV arrangement of the same geometry, so can I use the same sort of function, but have the donor-texture be a tiled texture rather than a UV-mapped one?

The second problem is that I want the texture to be an even size all over the model, not squished up super tiny on the smaller faces and stretched out on the larger faces and confused on the triangle faces. Is there a function I can use that would fit it fairly uniformly to the overall mesh rather than scaling it according to each face? But at the same time as that, could it be convinced to match up the tiles correctly, or would so many minor scaling and stretching decisions just be a little too much to ask of the software at hand?

If so, is there any 2D software anyone could recommend that could do sort of an intelligent pattern-fill and stretch itself around a vector contour rather than just cookie-cuttering it out (the swatch I made is vector to start with, if that matters or is useful)?

UVs torso
UVs limbs
Seamless tile

You can bake your texture to a new image by unchecking all the other textures but the one you have loaded, and that way you just catch the one into the bake, then save as a completed image. Be sure to reference that uv when you use it then.

If you just set seams and unwrap. you should see a really close result that you can then tweak with the sculpt controls in the uv image editor.