I would not go AI, minimal gains for the hassle. I would also give consideration to 9.3x62. Not absolutely convinced a 338-06 gives a lot more than a heavily loaded 30-06 (with 200 partitions as an example) if you run one of the lighter bullets in the 338.
One thing I found was that a fairly light gun (8lbs) shooting a heavier bullet (35 whelen, 250 grain) kicks a fair amount, at least more than I anticipated. Doing it again I would not go lighter in a medium bore and would likely go either 35 whelen (more versatility when downloaded, i.e. deer in the timber or plinking loads) or 9.3x62 if I thought I was up to it..
