I have seen quilts hooped and FMQ, don't know why it wouldn't work for SID too. You do need a hoop that easily fits in the throat of your machine, and hooping often is the only drawback.
Maybe slightly stretch out your quilt back by pinning or taping it to the floor, then sandwich and baste. This keeps the puckers out of my quilts, as well as using a walking foot :D:D:D