my opinion here:
I would NEVER cut my arrows without there being a reason(too weak).
I would bet you can get the .340's to work. Some simple fixes would be buy the longest .340 you can(i'm pretty sure that would be the black eagle vintage arrows coming in at 34"), so you'll have the most tunability and slowly trim the arrow as needed.
I would also bet that with a side plate adjustment(thicker or thinner), you will be able to get the 31" arrows to work, if you choose to cut them first.
When you're tuning, just remember you're worried about where the arrow is hitting in relation to center. If its to the right(RH shooter), build out the strike plate some(very small amounts at a time(1/64 or so at a time). If it's to the left, you can try a thinner or softer strike plate.
I have quit bareshafting as my primary method of tuning and started tuning the bow to the arrow. If it works out, it is great! If not, i go back to bareshafting.
Sorry for the long response, I hope it was helpful.
God Bless,
Daniel