Edit: You can load the -06 down...the question is how well will your particular rifle shoot with starting loads under 130-150 gr. bullets.
It seems to me the slightly slower 1:11 twist should handle the smaller bullets better, actually, assuming that it works the same in .30 caliber as it does in .223 (i.e. slower twist for light bullets, higher twist for heavier). As others have mentioned most .30-06 and .308s have 1:10 twists, and tend to like 150-180 grain bullets best.