Cheap = the roloc discs and/or the 3M wheels. I've done the wire wheel and it's good for 10 minutes, then the wires lay over, slowing the process and they start shedding. This is how I've done the last 2 compartments.
Faster = blasting, but you gotta really work to get all the stuff out before prime/paint. This is what I just had done to my entire van body.

Stripper is something I don't have a problem with on large surfaces, but an engine compartment has too many crevices and pinch welds. They will hold the nasty in and can bleed it out after paint. I did this on a car many years back, but did not use it in the jambs and other seamed/welded areas.