You can give your box the "Pin" behavior (instead of "Platform") and check for overlap with an image point to the side of the player. Here's something I put together (sorry I couldn't figure out how to embed the images):
The first link shows the object properties, including a custom collision box for the ... box... and the new image point for the player. The second link is the event sheet.
I did notice some jitters if I have pixel rounding turned on or if the player has too high of a "pushing" movement speed. In the second case, I think the solid behavior is slowing down the player before the box moves from the pin behavior.