Recommendations for .22 Ammo at 40-plus Yards on Crows. etc.

Sounds like you need more practice . I don’t mean that with any disrespect. If shooting at a live animal pest or not , I need to have complete confidence that it will be an ethical kill and that is with shot placement . When you spend enough time with said rifle and are able to hit a quarter at your intended hunting range ten times out of ten . Your ready for hunting , until then I would stick with practice . 
 
@Hobbyman2007 -- there is no doubt I could always use more practice. However, if I wait until I "have complete confidence that it will be an ethical kill" every time, I probably wouldn't shoot anything. So, at least for me, disabling the "threat," even if by wounding at first, is more important than having an "ethical kill" every time. I'm only human and doing the best I can.

Thanks for the feedback.
 
The answer to your question really isn't about your equipment but rather learning about how crows/ravens are put together. I have come, over the years, to really respect the intelligence of corvids, I think too much. After watching the Isle of Wight video of them killing the baby lambs being born, I have been reminded how that intelligence is also a negative. Hunting them actually kind of helps them stay sharp too so I also have been talking myself back into pulling the trigger on a few. Your Hatsan and pellet choice are good. I have taken 90 percent of all my shots standing unsupported too. I only recently got into PCP. For over 35 years I have been shooting a pair of .177 FWB124 airguns that are only 12FPE. The Brits will tell you that you can learn a lot from them and what they do with 12FPE, and they are right, but arrogant to say so ;) Anyways, I have taken full sized birds at 45 yards with an 8.3gr pellet, and no, it wasn't a head shot. Like everyone has been telling you, their feathers are tough, but they also have a grain. Never try to shoot one from the side through its flight feathers. You probably need patience has much as practice and that is really hard to learn. Pick your shot, the head if he presents it, the chest, if you are below and can place the pellet on either side of the sternum without going through the full chest muscle, or controversally from behind right up the kiester. The last way results in a death glide like pidgeons do, not pretty but works. This advice works with a 12fpe gun, you are using 30fpe, so you shouldn't have much problem at all. By all means buy a range finder, download Strelok app for your phone and learn it. If you can't afford a good range finder that gives you the angle, download a level app and use the edge of your phone. Yes, all of this takes time and you will give up some shots to it at first but it won't be because you are missing.