I used to be an auto detailer. Make sure you cover the fuse box, alternator and battery with big zip locks . You should use a variety of scrub brushes in different lengths and shapes to scrub all the dried mud staining off. If the simple green isn't strong enough try old school Gunk engine degreaser. Use the simple green or the Gunk liberally as in a lot.
Either way, wet the engine compartment first then spray with the cleaner, then scrub throughly, then rinse and let dry. I let the Jeep sit in direct bright sun light with the hood all the way open (resting against the windshield) to dry it out. Never once had a problem. You may have to repeat several times to get the desired effect and don't forget the underside of the hood.
Hope that helps