I’ve done a lot of bobbin drawing while quilting on my art quilts, but I usually do so because I want to use a decorative thread that is too thick or too lumpy to go through the needle. I also FMQ quilt on a domestic, so if you’re quilting with a walking foot or using a long arm or domestic on a frame, the following things may not apply.
The things that work best for me for avoiding bobbin thread issues are having my tension adjusted perfectly for the combination of quilt sandwich and threads and always bringing the bobbin thread to to top and holding both threads when starting.
As for couchinf the backside while you’re quilting, that will depend on if you’ve got a couching foot that has a guide hole that is a really food fit for the size yarn or cord you want to use. I do a lot of couching as well, but seldom do it using straight stitch because none of my FMQ feet have holes that reliably keep the couching yarn/cord in the middle where the needle will always catch it. As a result I usually use a zigzag stitch when I’m couching, which would then show on the top of your quilt as a plain zigzag if you are quilting from the back.
Rather than couching something to the back while quilting, I think I would use multiple colors of thread in the top to add color to the backside, or maybe use inktense pencils on it after the quilting is done.
Rob