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ScratchX was made to remove minor surface scratches. Most likely unless your spiderwebbing is minor, a touch up or repaint is in order. If they are minor you might want to take it to a well respected detailer to see if they can machine polis (buff) it out using an abrasive.
The webbing if fairly minor in most spots (and can only be seen in the right light). Maybe I'll should still try this, and see if it does anything? Or, in your opinion, do I risk worsening the sitation (and I should go directly to a detailer)?
You can try ScratchX, but I have never had any luck. If you want to try something yourself first, I would recommend 3M 39009 Scratch & Swirl Remover. Aplly it to a clean 100% cotton cloth and rub it into the surface. Do not let the product dry. Keep rubbing until the product disappears. In my opinion, that is about the best you can do without a machine in the hands of an experienced user.