That would be the way to do it. Swap the injector with another cylinder and see if the problem moves with it.
My bet is replace the injector, problem solved. But only after you are darn sure the plug is firing at full strength. The swap will verify this. Don't forget to replace the wet plug after the swap and before you fire it up. It might be so wet that it won't fire no matter what you do.
Then check your
oil to see if it smells like gas. If injector staying open, could be washing down the cylinder walls and diluting the
oil. Time for an
oil change!