can you post what you have so far? You only need the one move safe object, as long as you've added them to "protection" - the order of events is important, so make sure you look over everything in the event list editor too, not just the event editor.
I got it to work with a strange combination of events. Both the Move Safely object as well as my own storing of X and Y values in Alterable Values for when the player isn't colliding or overlapping with the background. Maybe it's overkill to have both like that, but it's the only way I got it to behave.