Get a couple of toilet brushes too - with the stiffest bristles you can find.
Not the horse shoe shaped kind (with the bristles wrapped around the wire). The kind with the bristles sticking right out of the center shaft work best.
Rough up the surfaces of the grime with the brush before applying the oven cleaner (or any kind of degreaser for that matter). This creates cuts in the muck and lets the solvent penetrate past the surface. It speeds things up.
Also, after applying the solvent (but before rinsing it away - maybe halfway though the application) scrub the grime with the toilet brushes. You get much more mileage out of the solvent that way.
Since we are on the subject of degreasing/cleaning the engine compartment (and anywhere else that has caked on grease) - here is the biggest assist I have ever found:
Use really hot water to wash, rinse and break up the grime.
Get a good quality garden hose (cheap ones will develop bulges and burst if used to supply hot water). Check the labels carefully, they will say whether the hose can withstand hot water. Home Depot sells a great Goodyear heavy-duty hot water rated hose for $30:
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It's real rubber with quality fittings and will last you a lifetime.
Hook it up to a hot water supply. I have plumbed a couple of boiler drain type valves into my hot water lines. But you can use the hot water valve that supplies your washing machine.
Avoid using the drain valve on the bottom of the water heater. It will accept a garden hose but a couple of problems:
The cold water dip tube that replenishes the used hot water goes right to the bottom of the tank. That's right next to the drain valve. So when you tap off the bottom of the tank the cold incoming water is drawn into the drain connection. You lose that real hot water fast.
Another problem is that when you are all done and want to shut the drain valve - it sometimes does not close properly. The drain valves supplied with water heaters these days are almost always cheap plastic. They are designed for one time use - to drain the tank for disposal.
For the few days that you are cleaning the truck, turn the water heater all the way up. That 170 degree water really helps loosen the caked on grime and wash it away.
Tell your household that you raised the hot water temp- the showers will get real hot if the handle is in the normal position. And don't forget to lower it back to normal when you are done cleaning - your gas/electric bill will shoot up.