I'd think stingers and other hyper velocity might scrub velocity fast and not be super stable.
For 500 yards I'd think you stick with standard velocity so as to avoid upsetting the bullet when the shock wave catches up. Unless if the goal is to just make it out to 500 yards with no real limit to accuracy. In which case, blaze away.
FWIW, 9mm can go 1,000 yards out of a handgun, so 500 yards with a 22 should be a piece of cake. Right?
2011 Toyota Camry, base, 2.5L/6MT, 205k, hers 2010 Toyota Tundra DC, 4.6L/6AT, 159k, ours 1999 Toyota Camry LE, 2.2L/4AT, 225k, his
Fast wont help you at extended range, you need the most consistent velocity you can find. I have never tried 500 yds but regularly shoot at 300. The heavier the bullet the better. 42 gr Eley force or Contact have both been good performers from my rifles. Force being faster requires a bit less elevation but not much and sometimes seems to be more wind sensitive than Contact. You are going to find that Lot # and ES will mean more to you beyond 150 yds than max speed.
Your exercise sounds fun. However in order to learn anything from it you will need more consistency than off the shelf .22 will afford. There is no doubt that the little 40 gr will make it there, but how will you know if the wind was the reason for a miss, or just inconsistent ammo?
I watched an old guy at the local range put 20 rounds of 22 LR in 3" at 100 yds....with a Smith&Wesson Semi auto PISTOL! Needless to say, he was not using just any old 22 rimfire ammo.