The issue I’m encountering is that I’m forced
within the 0-1 UV space, which significantly reduces resolution because I need to tile the fabric to make it look realistic.
You can make a small area of texture specifically for seams and overlap them there. As an example you have some space on the top of the texture which you can occupy for tiled seams texture.
Obviously seams should be straightened up for this.
I dont think you really need a bake for those seams. You bake the sofa since you need a normal map for cloth wrinkles, and texture for seams are just generic texture layered on top of the bakes.
So your whole texture set would be a combination of unique texture + 1 picece of “trim sheet” tiled on X axis.
Not sure what UV part corresponds to what geometry section in your screenshots, but you can reuse repeating parts as shared UV patches which will provide more space utilization.