The chances of this happening are probably slim. Most hotels are franchises. It's unlikely that the original hotel will agree to break a contract just to help out a nearby competitor.

I can't picture anyone at Starwood Corporate/Central Reservations that you can call reach via phone will have the authority to make this change. If you want this to happen, you need to call the original hotel directly. I wouldn't expect much, either. There's really no compelling reason for the hotel to cancel a non-refundable reservation in this situation. (I'm not trying to be harsh. That's just the reality of the situation.)