As @Nick Whaley suggested you can hook the process, but you don't have to go crazy looking for specific windows. You don't have to do that at all. Instead of going the windows route, you can hook CreateFile API, create a custom Action somewhere that would attempt to save a file in a predefined (possibly non-exitent) location. In your hook function look for CreateFile calls where with that special path/name of the file, and display your own save dialog. Call real open file with desired path, and return a handle to PS.
You will need:
- MS Detours Express
- About 2 hours of time
PS. Assign a hot-key to custom PS action, and use it to save files.