Ti,
I also own an Airhawk and initially had a few issues with it. The main thing is that the gun is pretty powerful at around 16 fpe or so, and tended to vibrate the stock scres loose with regularity. The barrel on mine not only droops but also locks up a little off axis left to right. So, out of the box, it was a bit frustrating. My iron sights were good, so I never experienced the problems that you mention. Here's how I fixed all of those problems and now have a gun that will hold it's zero and keep things on a quarter out to about 35 yards when I do my part.
First, I disassembled the gun and performed a basic deburring and lube tune with proper lubricants. That smoothed the shot cycle a bit and made cocking go much smoother. I also polished the bearing surfaces on the trigger group and lubed them, which helped reduce the trigger pull. It still has a good bit of creep in the second stage, which I might refine once squirrel season finishes in February. Or, I might just practice more as there are lots of fiddly bits in the trigger group and crawling around in the dirt and dust searching for escaped springs isn't my idea of a fun time. That's the voice of experience by the way.
The lube tune helped to calm some of the vibrations, but it would still loosen stock screws. So, I replaced the forearm srews with good hex-head bolts from my local hardware store. I also replaced the lock washers with regular flat washers. The bolts will hold much better and the flat washers distribute the load across the wood fibers which means you can crank them down more tightly without damaging the wood itself. The lock washers that came with it were hogging out the wood in the forearms. When replacing them, it's best to clean all of the oil from the screw threads on the bolt as well as on the action itself before installing. This will often be enough to keep the bolts from unscrewing under vibration. To be safe, I loktited them down as well. Every time you adjust the screws, your point of impact will change, so the loktite is a good idea as well. Though, it's best not to use it if you don't have to as it's kind of hard to clean up should you need to disassemble the gun again.
The leapers scope you chose has a good reputation, but you'll probably need an adjustable mount if your gun is like mine. I had to compensate for droop as well as the barrel itself pointing to the left. You can shim the rings with 35mm film if you have only a little droop, but you'll need to be careful not to use too many shims and end up bending the scope's tube. I bit the bullet and got a fully adjustable mount and that did the trick. It's vitally important for best accuracy that you optically center the scope and then use the adjustments in the mount to get on target. That gives you the best chance of keeping zero. The internal adjustments on scopes are prone to floating as they approach the limits of travel on their adjustment mechanisms. The symptoms of scope floating is one where the zero wanders around during a shooting session. Of course, that's not the only thing that can cause the zero to wander. They'll also wander if there is a temperature difference between the gun and where you're shooting such as if you keep it indoors at night but shoot outdoors mainly. Or if you aren't achieving a good, consistent cheek weld there will be some parallax even in an AO scope.
Folks touched on the importance of hold above in the post. My AirHawk is extremely hold sensitive, so I have to really concentrate on achieving the exact same hold from shot to shot. I get the best results with the forearm laying on my open palm just in front of the trigger guard and no fingers touching the sides of the forearm combined with a very loose hold where the thumb on my trigger hand presses down just behind the safety while the trigger finger itself moves up towards my thumb in a squeezing motion. My trigger hand fingers just barely cradle the pistol grip and the elbow of my trigger arm has to be almost straight out from my body. Something as simple as laying my thumb over the wrist of the stock will move the point of impact by an inch at 20 yards. The same is true for how firmly I pull the rifle into my shoulder. In the woods, this means that I'm mostly limited to shots as low angles where I can get my body into a good position. So far, I've only taken one squirrel at a significant upward angle, and that was luck on my part as the pellet impacted in the middle of his back when I was holding on his ear almost two inches away. I like the rifle, but it's far and away the most hold sensitive one that own. The prescription for that malady is more shooting practice, which is the kind of problem that I like :-)
I have also found that this rifle exaggerates any mistakes that I make mentally as well. So, if I forgot to control my breating, boom the pellet moves around. If I haven't achieved a natural point of aim, it's a miss. Pull the trigger rather than squeeze it, miss. You get the idea. Mind you, I'm a much better shooter in some ways because it's forced me to become more deliberate about my preparations, but the learning curve has been frustrating.
I shoot mainly heavy pellets in it as I find airguns to be most accurate if you shoot around 900 fps max in order to avoid the pellet passing through the transonic zone closer to the speed of sound. So, it's either JSB Heavies (also sold as Air Arms Field Target Heavy) or Crosman Premier Heavy. Beeman Crow Magnums might be a good candidate as well, but It takes pellets in the 10 grain region to keep this thing under 1000 fps, so that's what I use. I just reread Tom Gaylord's review of the AirHawk Elite and he's getting much lower velocities than I remember for this powerplant. Hmmm, looks like I need to break out the chrony and retest as I may have been seeing the effects of dieseling the first time around. More shooting :-)
In summary, my AirHawk is hold sensitive with a droopy barrel and the trigger won't be mistaken for a Rekord any time soon. On the bright side, it's very powerful, priced right, and not so precious that I feel bad about dragging it through woods and weather. What's not to like?
