Before you extrude, make the whole line, then bevel it. Now it has even thickness
I don’t know about polyquilt, but does it work if you hide the seam’s vertices? That would work with a lot of tools in Blender.
If it can’t be done with polyquilt, it could surely be done with loop tools. It would be a bit slower, as you would need to select the loops to work on, but you can work on very specific sections of a mesh with that addon and it does have a nice relax tool.
You can also assign different Face Sets from edit mode selection and use Relax Slide sculpt brush with Face Sets auto-masking.

