This is a late reply, I know, but FWIW, my 340PD is spot-on with the special "snubby load" Gold Dot 135gr+P JHP, which was designed from the get-go to hit to the very same point of impact as the traditional snubby load, 158gr +P LSWCHP, in 1 7/8" barreled J-frame revolvers.
It's much more accurate and precise with this load than with ANY of the 125gr +P JHP .357 Magnum loads, which seem to be less stabilized in this gun, and also have lots more muzzle blast and flash as well as punishing felt recoil.
I use Crimson Trace laser grips on mine, makes an ideal little pocket gun.