No matter how low I set the air speed (20% now), small stuff (0805 or smaller) keep flying away, and I have to crank up the heat up to about 330°C to even have the chance of the solder melt.
Still too high air speed, I guess. Or maybe you hold the nozzle too close to the parts.
I have one of those cheap (but good)
Yihua 8858 hot air guns and am having good success with soldering SMD parts, including small ones. Settings: air speed 15% or even less, temperature 360 °C or even more, calibrated using a DMM with a thermocouple. High temperature, I believe, is not much of a problem, as long as I don't hold it there for too long: basically just enough to melt the solder, and in some cases to give the part a little push or two and watch it snap back into place to make sure it's properly seated.
Preheating (just hit the board with hot air from the bottom for some time) also helps.
Regarding high temperature: I've had some ICs that I initially soldered with an iron, then desoldered using hot air at 360 °C, then soldered back again with an iron. Of course I can't be certain that they definitely weren't damaged, but at least they kept working as expected. As a matter of fact, I have never made a semiconductor component non-working during soldering or desoldering. Whether I created any subtle damage, I do not know.