Regulars here know that I'm a real fanatic about engine compartments (among other things), and I've accomplished this kind of clean up many times, usually on very used vehicles that'd never had such areas cleaned before (e.g., the '93 Audi was so filthy that it looked like the underhood surfaces were all spraypainted black when I started).
Besides APCs, i sometimes find a steamer helpful, but not as often as I'd expected. Let the APC dwell for a good long time and agitate it with a brush (preferably one with natural bristles, they seem to rinse clean of nasty grease-crud better than synthetic ones).
I do a lot of cleaning with solvents- no rinsing and they really cut through greasy stuff. ValuGard's New Car Prep is great and it's *VERY* safe. Keep the solvents off decals though.
For the "white corrosion" on zinc/etc. plated surfaces I like Wurth's Rost Off. There are other products that work well too, but whatever I use I work the surface with something like a brass brush or a ScotchBrite pad, or ValuGard's Bug Pad.
I clean black plastics and rubber surfaces with Griot's Rubber Prep (freakin' miracle product) and usually treat/maintain them with ValuGard's FastFinish (if I don't bother sealing them with Ultima's sealant first). I sometimes treat prone-to-oxidation rubber bits with Wurth's Rubber Care but otherwise I pretty much avoid dressings altogether.
Rinseless wash products (I'm currently using Garry Dean's Infinite Use Detail Juice) are always handy for areas that aren't too filthy.
Painted metal is just like the rest of the car- polish then LSP. For tough-to-access areas I like Garry Dean's Beyond Infinity Sealant.
Matte/Satin-finished black metal bits- of all things, I find that Blackfire's gloss enhancing polish works incredibly well! Even if the parts in question have a little surface rust. Their sealant isn't bad over top of the polish (which leaves some stuff behind). If such surfaces are in *really* bad shape (but you're not gonna refinish them), try AutoGlym Bumper Care...yeah, their stuff for black plastic trim! Sounds weird but it really works well (e.g., I used it on the rusted, nasty hood springs of my Tahoe, and years later they still look OK with minimal upkeep).
I mentioned the natural-bristle brushes earlier, and I use a lot of them. Trick for this application is to get ones that stay a little firm when wet (but keep those off painted surfaces lest they mar). And I use swabs. A *LOT* of swabs. I probably go through over a dozen even when just doing a quick maintenance wash, so you can guess how many I use for a big cleanup!
MidShipExpress- Your Toyota sounds like just the sort of underhood (and undercarriage too!) project that I go nuts over! I understand compeletely the look you're after, so if there are any specific aspects of the job that have you stumped, post back and we'll see if I can help any.