I have a .240Gibbs which is pretty much the same as the 6-06AI, only more. The very accurate load was a 70BT4100. I mention it because this was only a moderate load and the 6-06AI should do that without a problem. Maybe give you some idea about what to expect from heavier stuff.

Addition: Should have also said the barrel is Pacnor 28", 13 twist. This wasn't a wimp load but also not near top end.....4831 powder. The gun now has a 6mmAI Krieger barrel. Used strictly for rockchucks.