I have reloaded for the 30-06 for a few years (since 1972 as I recall). 1:10 should stabilize anything from 100 gr to 220 gr. IMR and H 4350 work well for 150-220 gr bullets in my experience. Your results seem unique. Be certain to check all your fasteners, ie, action screws, scope mounts, etc.
I currently have a Kimber Montana 30-06 I am having trouble with that I bought from a LRH member. For some reason the 24" barrel had been cut from 24" to 23". After wasting a bunch of factory ammo and reloads trying to find a load I started looking things over only to find the muzzle crowning was awful! I have an order in to PT&D for a 45* crowning tool to see if that helps. You may have the same issue.
FYI the heavier bullets shoot better with the bad crown than the lighter ones in mine.
Also John Barsness has a good article called something like "getting the most out of your 30-06". It may help you work up a load.
I load from 100 gr Speer Plinkers to 200 gr Nosler Partitions all depending on what the task is. The 30-06 is still a great universal cartridge IMO&E! Don't give up on it!