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Replaced my speakers as well and was wierded out the whole time about what you are going through. So much so, that as a precaution, I bought a tube of Dow-Corning Structural Silicone. It is a "caulk", but designed for commercial curtain-wall installations -think glass, high rise office buildings.
Fill the stripped-hole on the back-side of the inner fairing (out of view) with a SMALL amount of the silicone, get the outer fairing lined up with all other screws in place, place the stripped screw in place and tape the outer & inner fairings together. Allow the silicone to cure thoroughly - it is temp and humidity sensitive.
Be very careful not to use too much, because it will be a bear to separate the inner and outer if you do. It might be a good idea to use some painters tape between the 2 fairings.
Dude - Hope this helps.
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