My computer is down right now, so I'm having hard time explaining and testing, sorry.
I wouldn't use a sprite for the grid, but a tiledBackground, as it's the same sprite repeated X times. With a single object to move, it would be easier.
If you need to keep N sprites for any reason, then you'll have to add a different offset for each one, and keep track of witch cell is witch (lots of events/variables for this though).
If you don't use an every tick, how do you do it right now ? a condition "Player.plateform Is moving" could do it (witch is also an every tick with a condition by the way).
Hope this helps, I'm trying my best ^^