I think your twist rate is a mistake, if truly 1/11"! The standard for .30/'06, as you probably know, is 1/10" (same as for the .30/40 Krag usiung 220 grain round-nose bullets of 4.5 calibers in length), but some have been made 1/12" to shoot bullets up to 150 grain weight more accurately than the faster twist is capable of.
There is a story from Springfield Armory of an instance in the early days of the 1903 Springfield when a particular run of rifles was showing unusual accuracy in testing after manufacture. Investigation as to why these guns were so accurate finally revealed that the rifling machine had "slipped a cog", and was cutting 1/11' twist barrels instead of the 1/10" twist that was the milspec. (Your 1/11" twist conforms to this finding!!) Well, the Army soon corrected this "problem", and had the machine back to making "correct" barrels quite soon, despite the fact that the "bad" ones shot better!
As you may know, required twist for any given bullet depends on the LENGTH of the bullet, rather than its' weight. The Greenhill formula will let you calculate if your twist is fast enough or not, but you must measure the
length of the bullet to use it. This formula specifies that the required twist,
IN CALIBERS, is equal to 150 divided by the length of the bullet
IN CALIBERS. Using this formula, I calculate that a .30 caliber bullet of 1.25" in length should be spun by a twist of 1/10.8", which should be close enough to your 1 in 11" twist to work. If you used no bullets that exceed 1.2" in length, you should be O.K., no matter what they weigh. Of course, a streamlined spitzer of this length would weigh quite a bit less than a blunt or round-nose slug of the same length.