Is the OAL length 3.340 or 3.440 for the 338-06 and the 338-06AI? I've read articles and read books that say it's one or the other. Anyone have experience in this area?

Normally I see 3.34" I have seen some reference to the 338=06 A Square as 3.44". http://www.gunsammo.ws/338-06-A-Square.htm
Since they were the ones to make it commercial they could set it anyway they want. Some actions would allow the 3.44 some won't. Normally since the 06 baased case usually has an OAL of 3.34" that is what is used for the various AIs as well.

If it your rifle you can set it anyway you want.