Can you place a large flat sheet on the floor and spray baste the sandwich that way? That is how most people do it.
I guess I do not understand why you are spray basting the backing and pinning the top.
I don't like to stretch the backing fabric at all, whether spray basting or pinning. Stretching allows the backing fabric to "spring" back when the clips are removed. It is only necessary to smooth the backing fabric, not stretch it. I'm thinking that the puckering you are seeing in the backing fabric now is probably from this, which means that you now need to stretch the backing fabric again until the puckers are gone. This means clamping the already finished portion of the quilt to one side of the table, then stretching and clamping the remaining backing fabric to the other side.
So, the short answer (if I am understanding your question correctly) is that yes, you do have to anchor the quilt all the way around for each section.