Molly suffers from SA as well. Except she has never displayed symptoms of soiling in the house or crate.
We tried keeping her in a small room, since we really didn't want to leave her in her crate for hours at a time, but she managed to destroy anything she could in that room, including shredding the vertical blinds up and pulling the closet doors off
after that incident, we decided that the crate is the safest place for her, even though she doesn't really like it. She even figured out how to lift open the crate door and get out and reek havoc on the entire house, so we have had to reinforce the door with clips. Have you tried an appropriately sized crate? one that is large enough for her to stand up in but not big enough for her to want to poo/ pee in? I really think that would be the safest solution. The last thing you would want to come home to is an injured dog because she got into something she shouldn't have