I think the idea of stabilizing the knit/stretchy fabrics BEFORE cutting them is the better idea.
Then when you cut the pieces they will stay the same size while you work with them.
You might want to stay with approximately the same fabric weights, though. For example, I don't think I would use a heavy denim with a lightweight nylon sheer.
If this is to be a quilt to be "loved" and used, then why not use familiar fabrics?