I have two 340PDs.
As I've posted here before, I've shot nearly every commercial premium brand of .357 Magnum JHP through them, a minimum of 20 rounds of each, as well as all premium commercial .38 Special+P JHP loads.
It's "OK" to do so, in the sense that it's safe. (It isn't pleasant with the .357 loads, but it's safe; the gun won't blow up.)
What yields the best combination of accuracy and precision is another story.
IME, no single .357 Magnum load produced as much precision or accuracy as the better .38 Special+P loads in these guns, with the Speer Gold Dot .38 Special+P JHP giving best-overall results, in my guns, in my hands.
(I'm not "recoil-sensitive", and I'm convinced that these little lightweight guns are actually more precise and more accurate with the better .38 Special+P loads than with any of the .357 loads.)
There's no way to determine what gives the best results in your gun, in your hands, but by trial-and-error shooting, but IIRC the Remington Golden Sabre .357 JHP load was acceptable, yet not as good as the Speer Gold Dot .38 Special+P JHP.
Best of luck.