[Christ]

It shouldn't get soggy at all... you can put shellac coating on it to waterproof it. (Shellac is environmentally friendly and edible when dry.. it's made from bug poop, though.)

I wouldn't do the lower ones, though... it might defeat the purpose, since your bottom grilles are presumably lower than the stagnation point. (Usually, you let the dirtiest areas stay dirty, and clean up the other areas.)

It might be in your best interest to start at the upper grille, then, once you're comfortable with it, block one part of the lower grille, etc.. until you start noticing the fan coming on more often, or noticing that your heater is hotter, blah blah blah..

You really should get an aftermarket temp gauge, at least. The OEM gauge isn't accurate at all, and will read normal in a range of ~160dF to 205dF before it changes position again.