If you are quilting on a frame set up, where you move the machine, then the below info doesn’t apply.
If You are quilting on a domestic or sit down- (moving the quilt, not the machine) then I would suggest being very diligent about basting if you use the satin for the back. I’ve found that satin tends to slide around a fair amount, even with spray basting. You can see this happening on the top and work to keep it aligned and wrinkle/pleat free but since you don’t see the back it’s easy to get a tuck or pleat. When I’m working with a fabric that is likely to slide a lot I like to spray baste, let sit overnight to set up and then pin baste as well, being careful to check both top and bottom after basting to make sure all is well before I start quilting.
it might also be easier to control the backing satin if you use a layer of thin cotton batting with a scrim under the wool batting. Wool batting is a dream to work with, but it is fluffier and more flexible than cotton batting which gives the fabric more opportunity to develop wrinkles while you’re working with it. Spray basting the backing to the cotton batting and letting it set up overnight would help to keep the fabric from slipping and getting wrinkles.
if you do use a double batt, I have had good luck spray basting the back to the cotton batting, then spray basting the wool batting to the cotton and then spray basting the top fabric to the wool using 505.
Hope you post pics of the quilt when you’re done it sounds lovely!
Rob