Yep, the 135 SGD will probably be the right answer. That's what I carry in my 340PD.
The long version is that the best projectiles for short-barreled .38s of all types are the Speer mentioned above and the FBI load, a 158 gr. LSWCHP +P. I would opt for the latter, but the 340 is so light that soft lead bullets at +p velocities pull out from the cases under recoil--a problem not experienced with jacketed +p's (or standard pressure lead bullets). All that to say, I don't know whether the Ruger has identical issues, but it would be worth investigating at 13.5 oz.
As far as the Hornady, looks interesting, but my gun is not supposed to use under 125 gr. bullets, so I don't. Again, don't know if the light Ruger has similar issues.