We use 90% lean beef for our hamburgers, (according to the packaging) but they seem to shrink in diameter (the size from one side to the other) and plump up like a  muffin.  So instead of and nice pancake type burger we end up with more of a meat ball.  That's a bit of an exaggeration but I think it conveys the nature of our hamburgers.

I wondered if I made a wood press to form the hamburgers if they would retain their shape.  Is there any method to ensure they stay flat?

These are grilled on a grill, not microwaved or pan fried.