Bigger beers also seem to have carb levels vary within different strata of the beer. In other words, the upper third of your beer is likely more carbonated than the lower third. Eventually it works its way through, but some folks over compensate and leave too high a PSI on for too long, so that by the time the lower 3rd is carb'd...the upper 3rd is over carb'd.
In lieu of shaking, try disconnecting the gas, bleeding pressure, removing lid and using a sanitized paddle to gentle stir and mix the beer a bit. I've had this happen a few times.
I think what I'll do it shut the gas off, bleed it off and then rock the keg from end to end to mix it up. Then set it back to 12 psi and wait.