AnarchyChess

I think E/F-3/4
That way, you need to slide a tile before playing King's pawn (I assume this costs the turn), meaning at the start of the game, white has to choose to either go for a normal E4 opening or to functionally give up the first turn in order to get a tile available on E3 & E4.
I don't know how this would affect Queen's pawn openings.
I saw this comic yesterday and thought about it for a while though; I think the game would probably be likely to draw by repetition as you are capable of undoing your opponent's last slide, referenced by the alt text:

The draw-by-repetition rule does a good job of keeping players from sliding a tile back and forth repeatedly, but the tiles definitely introduce some weird en passant and castling edge cases.

It would be fun to try out though. You could also add some rules to balance if like "you can't slide a tile if a majority of pieces on it belong to the opponent" or something