My bird is red, so I haven't noticed the "spiderweb effect", but I have bought/used Zaino and am very happy with it. Here is info about one of their products specifically for your "problem":
Z-5 POLISH FOR SWIRL MARKS & FINE SCRATCHES
FACT. The only way to remove, heavy swirl marks and scratches from a clear coated surface is to have the car professionally machine buffed with an abrasive compound. This should be the last resort, as factory clear coat is very thin and you can break thru it very easily. Also, most polishes and waxes contain abrasives, they remove some swirl marks but create new swirls. Kinda of catch-22. Z-5 is the first non-abrasive polish that will eliminate swirl marks, fine scratches and spidering, without hurting the integrity of the clear coat. It does this in stages, anywhere between 1 to 3 applications. This in itself is a major technological breakthrough. With each application of Z-5 polish, you will see the swirl marks and fine scratches gradually lessen, until the marks are no longer visible. Although this procedure may seem time consuming, the results are well worth it. This is the only way a swirl mark problem should be addressed and corrected.
Z-5 is the safest, most cost effective way of repairing the paint, so to speak. After you are satisfied with the way the paint looks. Switch to Z-2 Show Car Polish to achieve an even higher wet-looking, optically perfect paint finish.