I seriously hope some people read this, because they SUCK at grabbing neutrals, even as Vasari.
1) DO NOT let your scouts stand still in gas gaints and plasma storms. With proper micro, they should never die to the pirate defenders, or enemy defenders (minus fighters).
2) Queue a few movements (120 seconds worth) to regen AM, and then order it to capture the netural. If the grav well has more than one extractor, press shift and give it another movement order, and then shift and capture neutral order. Repeat for additional extractors.
3) Pin the grav well to your empire tree so you can see if enemy forces are trying to retake the extractors.
4) If you need to send a scout from a few jumps away to a neutral extractor, first order the jump to that grav well, then press shift and order a few movement orders around the gravwell. By the time the orders expire, it will auto capture a neutral and by that time you should be able to check back on it's progress and follow the instructions in number 2 above.
5) Use your scouts offensively. Yes, they have weapons people, use them.