Gordy. You're quite right. I stand corrected - on both points!
Claudia. As you say, the CFI's FAA license is not type specific, so it doesn't matter what aircraft you're in for the endorsement (so long as it's an N reg light helicopter under a gross takeoff weight of 12,500 pounds).
Equally, and on the same principle, once you have done the flight review (presumably in your Squirrel) and have the logbook endorsement you can then fly any N reg light helicopter under a gross takeoff weight of 12,500 pounds for the next 24 months (to revert to my original point), completely irrespective of your EASA type ratings...should you wish to do so...