For me:
Go .22. Much easier to have a large and inexpensive pellet selection, and the tradoff for the slightly smaller size is probably fairly negligible if you can do your part. The .177 is plenty powerful to do the job in many instances, and may have a better pellet trajectory, but arguably the .22 might be a better choice for your application.
The diana 460 magnum might be the same weight as the asp20, but I think the gun might be harder to find. Plus, the cocking effort is a little higher. If you are going to shoot round after round, that effort will add up. At 33 lb cocking effort, I literally have shot my gun all day long.
The hatsan 135 has a much higher cocking effort, and is a heavier gun. For my use, it would get to be a PIA. I will target shoot, paper, spinners and hunt all day long. I've sat and shot my asp20 airgun HUNDREDS of times at my range in my yard (with spinners and paper and targets out to 40 yards) in one sitting no problem at all.
The asp20, to me, might be the gun of choice. The weight is not bad. Cocking effort light, muzzle FPE is great, and accuracy for me is stellar. Plus, its easy to find, the price is not bad, its backed by a large company with government contracts, and if it gets a bump here and there you won't twitch about it.
Downside is you won't be able to tinker with it, but I have my other guns to tinker. Parts? I havent needed any, and I'm near 10,000 rounds with no signs of any mechanical wear or problems whatsoever. My lockup needed oiling. Thats it. It destroyed 2 scopes. If I want to tinker, I have my dianas, hws, rugers. This one I treat like one of my firearms.
Today, 40 yards. .177 DRT. No supports, off hand.