Currently I am shooting 340's but there seems to be a quite a bit of wobble in the arrow. Should I be shooting 400's instead?
If you think your arrows have a wobble in them now wait till you see what the 400's will do
The 400's are a softer spine than the 340's and there is no way your going to get them tuned for your set up.
Have you tried lowering the poundage of your bow?
Is there any fletching contact?
What arrows where you using before switching to the Axis and did you retune the bow when you changed?
The 340's should be the right spine for your set up.