If I was a betting man....(bahaha) I'd be giving Tim all my money.
Actually, today I am looking at some low toxicity
(Non Methylene Chloride) chemical paint strippers. Much along the lines of Lloyds Fight Back graffiti removers that will spray on and wipe off in just a few minutes to take off spray paint and should leave the original finish (leave on overnight for a complete strip). Not sure that will work on the inner fenders, but the cling to version should work excellent on the frame rails, as well as all of hard lines w/o the need to remove them completely. Maybe giving the lines a brushing to loosen thicker material and recoat but might work well. Once it's done the work, it simply washes off with water to neutralize it. All of the hard line clips could then go into a bucket of chemical paint stripper to soak and remove the paint. These two processes might clean things up rather nicely. Products come bulk form or in aerosol cans and it's definitely worth a try.
I'll know how this works later in the week as I plan on testing a couple products first. If it works on a couple spot tests. I'll get the bulk material and go to town on the underside.