Best de-greaser for old caked-on oil/dirt?

You may find an outfit which steam cleans (heated pressure washer) trucks or something and have it done. There used to be plenty of places which had a rack for your car and they would stand under it and steam clean the underside. Since you are in SOCAL I would look out in the desert where the rednecks and truck-rodders live.

DIY, Wait till hot summer (so things will dry after). Rent a steam cleaner pressure washer for 250 - 400 bucks. Jack car up 4 feet off the ground using tall jack stands or what ever. Proceed to blast.
In the engine bay, when blasting up from underneath, lots of gunk will end up all over your engine and engine bay so you'll want to then open the hood and wash the area out after you do the underside.

Steam cleaner will remove all traces of gunk. If you put it 4 inches away from the surface, it will remove undercoat too. Wear an old raincoat and get a few pair of chemistry goggles cause it is a messy job.