You want to avoid any product that saturates the surface of the MDF - that face will swell, causing the whole piece to bend in the opposite direction.
Solvent-based products - that evaporate quickly - will help minimize this. A couple of coats of spray varnish as a base-coat will protect the material from swelling. If you can, apply whatever product to both sides at the same time.
A trick I learned while painting (full-sized) cabinet doors is drying things on a nail-board - pound a dozen or so thin brads or nails through a piece of plywood or MDF so it looks like the proverbial bed-of-nails, then use it as a drying rack for pieces painted/sprayed on both sides. Don't forget to get the edges at the same time, too.
Once your pieces are sealed, you should be able to landscape them without much risk. Beware of thick coats of air-dry clay or PVA - those shrink slightly as they dry and can pull the piece into a warp.