I use a walking foot and I don’t have a problem.

I used soft flannel and sprayed it.
Also, used fleece. It makes the quilt heavy.

If I understand you correctly, you could either put a single large piece of stabilizer behind the whole top, or individually put separate pieces of stabilizer behind each section of top, blocks and sashes. One major purpose of the stabilizer is to keep the pieces of top from puckering or getting pulled out of shape while you stitch the top together, so I would lean in the direction of stabilizing each piece of top separately, including putting a piece of stabilizer behind each section of sashing. The thinner and stretchier your top pieces are, the more helpful I think it will be to stabilize each one separately. Hope that helps!