After shooting many, many thousands of the Berry's plated 9mm bullets through several different handguns, I can tell you they shoot just fine. I've run them through Springfield XD's (3 of them), Witnesses (4 of those) and Smith & Wessons (3 of those), all in 9mm. The plated bullets are made that way on purpose, since they're soft. There has to be something for the rifling to grip, or the bullet won't stabilize properly.
You'll do fine with plated bullets in .356" diameter.
Hope this helps.
Fred