Yeah, as if textured plastic trim wasn't bad enough by itself, let's make a part out of it with all kinds of nooks and crannies that you can't get into.
I'm not sure the steamer would be so dangerous...that cowling has to get pretty hot in the sun, especially with engine heat billowing out over it. Screwdriver....doesn't Danase sell some plastic sticks for wrapping MF's around? Obviously, a test of the Magic Eraser in an inconspicuous spot will tell you if it's ok (perhaps open the hood and rub on a portion that's covered by the hood when it's closed).
I always thought a part of the problem with this kind of trim in general is that it gets UV damaged, and the only thing you can do is mask it with oily stuff to make it look good. I remember crowing about some trim on mine that SG did a great job on...only to be scolded by Accumulator that once it got older I wouldn't be so lucky. I'm still lucky with that car, but most others this type of trim seems to turn whitish pretty quickly regardless of what you do to it.