In my humble opinion the only reason to run a 340 is if it is the original engine for the car, or if you are trying to build a high RPM engine from factory parts (and then I would want a forged crank version).

Otherwise the 360 is the way to go. Plenty of 360 LA cores still around, and just as many loose 5.9 magnums in junkyards. The heavy car will also appreciate the extra torque from the longer stroke.