You should be fine with the 5/16", but if you're putting in a new line anyways, I would go with the 3/8". With that said, I went from a 340 to a 440 6 pack with the original 5/16 line for a couple years with no noticeable ill effect, although I did upgrade to a 3/8 a couple years ago.
If the question is, do I need the 3/8 line, I would say the answer is no, but, what are your future plans for the engine?