The best way to avoid problems is to test the ammunition in your gun with your hands holding it. That way you can be sure that the ammunition will perform satisfactorily for you. In very general terms, jacketted ammunition is less likely to pull than lead. The problem can, and does, occur with both .38+P and with .357 magnum.
From personal experience, I have gravitated to Georgia Arms 125 grain Gold Dot .38+P in my 342. They are securely crimped and have never pulled in my gun with me shooting it. For that matter, I have never seen them pull in anyone else's guns either. When I see some of the Speer 135 grain Gold Dot loads, I will likely buy some to try them based on my previous experience with their bullets in the GA ammo.
So how do you like your new 340? How are you carrying it?
Clemson