Well, I've never had much trouble with the autogyros on the first Hollywood mission; then again, I tend to pack nitro so I can just outrun them. However, you may want to try hitting them on the ground. They're sitting there on their little parking lot, and it's possible to shoot them up and destroy them before they take off. I usually manage to get one or two before they take off just by taking shots of opportunity with .70s and rockets.
For the Sky Haven autogyro mission, I'll share a tip I saw in an online walkthrough. Apparently, going through the 4 locations in a certain order are more likely to cause Booth to appear. This walkthrough recommends going to the Brothel first and then going to the Bar by the Dry Docks. I've used this myself and I've found that there's about an 80% chance that this will cause Booth to come out, with a small chance that he's at the Brothel right away. The best part of this is that you only have to fight two Brigands. If I don't find Booth at either of those places, I typically just restart the mission.
The walkthrough can be found here:http://www.gamefaqs.com/pc/914280-crims ... /faqs/9275
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