..........Some of the 40 gr. stuff (even high velocity) seems borderline for proper cycling and the lightweight hyper-velocity loads are even worse...........
Sounds like your Beretta 21a might need a little TLC.
IE: The recoil springs/spring housings are full of pocket lint, rust, gunk or something similar causing the need for more recoil to cycle action.
I've got a Taurus PT22, which is a Beretta clone (more or less) that cycles okay on anything from a standard velocity .22lr up, including the light weight/hyper velocity stuff. I'm inclined to believe your Beretta ought to do about the same, but I don't own one, so I might be wrong.
At 25 ft, the 60gr stuff is as accurate as anything else out of a Taurus PT22 and a 4" M94 as well as a 3" S&W and a Ruger MKII Target 678.
At 25 yd, I get nice round holes with the PT22, a few slightly egg shaped ones from the M94 and an occasional keyhole with the Ruger. I haven't shot any through the S&W at the outdoor range yet.
I haven't looked into why it is (for me at least) less stable out of longer barrels (twist rate?), but my main reason for using it is low noise so I don't scare the cats as much when shooting in the basement.
One of the things that I have noticed with both the PT22 and Ruger is more blowback than usual when the case ejects, so be sure to have wraparound eye protection when shooting this ammo.