I think it's an idiotic notion not to believe that 2 mere cups of liquid are not going to be dilluted by the mere action of the UPWARD swirling of the beer as it is
You'll find that most folks who have "inconsistant" carbonation when we pursue it further it turns out they're opening their bottles too soon. It's quite easy to blame or assume it's because of something, rather than the truth.
I personally believe the whole "priming sugar didn't get mixed" argument is BS, if you put the sugar solution in the bottom of the bucket and racked your beer, then it couldn't help but be mixed. You're putting 2 tiny cups of liguid into a vessel and dumping 5 gallons into it and the beer is rising as it fills the bucket...believe me, it is mixing.
Most of the time when a beer is acting weired, it's just that it's not fully carbed yet. And if you're below 70, or were below 70 for any period of time during the 3weeks, then the beer hasn't fully carbed yet.
I have never stirred my priming sugar in a batch of beer, and I have never had a beer, that when I waited sufficiently long enough, has not been CONSISTANTLY carbed from bottle to bottle. I've had plenty that the first one hasn't been carbed, but then I don't go an open any more beers right away I usually give it another week and try again. But once that first beer is carbed, and it's been 3-6 weeks since I've bottled, I've never had the rest of them NOT perfectly carbed.
But hey, if stirring keeps you warm at night....have at it...but if you open your bottles too soon (and too soon can be 6 months for some beers) and they still aren't carbed up- then what are you going to blame?
This is one of those somewhat silly arguments that we've debated for years on here. I don't think it's ever gonna be solved til someone puts together a clear bottling bucket, brews a really light colored beer, uses multiple cameras and dyes their priming solution, and videotapes the stuff mixing as it fills.