removing the drain plug in the bottom of the boat before we reached shore ? ? ?

That's the SOP for draining a seriously swamped small power boat. With the bilge hole in the stern, any forward motion creates a reduced pressure around the bung-hole that effectively empties the boat - as long as your engine can run and forward motion can be maintained. Most outboards are intentionally designed for this to work (but try it out in shallow water if you're not sure).

Dropping the plug overboard or losing it in the bottom of the boat ... or killing the engine during the operation without the plug conveniently handy for quick replacement ... Now THAT'S A SCREWUP.

John