As as already been mentioned, longer arrows will reduce your point on hold or lessen your gaps if you're a gap shooter. Other than that, it's not going to make noticeable difference inflight characteristics.
That being said, I don't like arrows longer than necessary. For me that's 1 inch beyond the back of the riser at full draw to provide clearance from the broadhead. Longer arrows are just a tad more cumbersome getting from a bow quiver onto the bow, for example, especially in close quarters like a pop-up blind or some tree stand situations. Likewise, if you occasionally lean your bow up against a tree, the nocks of the arrows in the bow quiver, if you use one, will fill with dirt.
I've never found it necessary to leave my arrows long for tuning. If they're too soft, I just buy the next stiffer size, cut them to the length I want and put on the point weight I want. If I have to tweek something at that point, which I usually don't, I'll play with the side plate material a little.
If .400s aren't stiff enough, .340s should work. .300s are awffully stiff. Good luck with whatever you choose.