Letting the engine turn over 5 or 6 times will NOT cause the engine to flood. If you’re letting it turn over an excessive amount of times without starting, then yes, you will flood it.
Jesse, you should be ok with removing the coil. But do it PROPERLY. Don’t disconnect the cable going from the coil, remove the 2-pin plug from underneath.
Turn it over a couple of times, then plug the 2-pin plug back in from under the coil.
Proceed to start the engine.
Cranking the engine without the coil being plugged in is a proper technique when it comes to checking the amps being cranked for the battery/battery voltage drops.
I learned that from my AST class last Monday 