If saver space opens on STL-SFO, you should be able to change to it whether you're in the SDC window or not. There are no change fees for MileagePlus awards. UA reserves the right to charge fare differences to non-Premier members, but most saver awards still come in at a fixed price point so there's unlikely to be a difference.

I agree that an agent can put you on standby for the nonstop despite it being a change of routing, and while it's technically at the agent's discretion, it's an easy request to honor and one where I wouldn't expect pushback.