You bottled them last friday, they are nowhere near close enough to worry about it...why did you waste 2 beers?
Mixing's not the issue, patience is...the liquid of the priming solution, really DOES mix fine on it's own. The natural motion of the beer filling the bucket and rising up really is enough motion to integrate it together just fine.
You are mixing a small amount of liguid to a larger volume of liquid, and it's going to distribute itself equally just fine. It's not like we are adding dry sugar to our bottling bucket and mixing that with the beer....the two liquids mix together and the sugar water dillutes just fine.
Inconsistant carbonation,
simple means that they are not ready yet. If you had opened them a week later, or even two, you never would have noticed.
Each one is it's own little microcosm, and although generally the should come up at the same time, it's not an automatic switch, and they all pop on.
But they all will pop on when the time is right.
The
3 weeks at 70 degrees, that we recommend is the
minimum time it takes for average gravity beers to carbonate and condition. Higher grav beers take longer.
Stouts and porters have taken me between 6 and 8 weeks to carb up..
I have a 1.090 Belgian strong that took three months to carb up.
Temp and gravity are the two factors that contribute to the time it takes to carb beer. But if a beer's not ready yet, or seems low carbed, and you added the right amount of sugar to it, then it's not stalled,
it's just not time yet.
Everything you need to know about carbing and conditioning, can be found here
Of Patience and Bottle Conditioning. With emphasis on the word,
"patience." 
A tiny difference in temps between bottles in storage can affect the yeasties, speed them up or slow them down. Like if you store them in a closet against a warm wall, the beers closest to the heat source may be a tad warmer than those further way, so thy may carb/condition at slightly different rates. I usually store a batch in 2 seperate locations in my loft 1 case in my bedroom which is a little warmer, and the other in the closet in the lving room, which being in a larger space is a tad cooler, at least according to the thermostat next to that closet. It can be 5-10 degrees warmer in my bedroom. So I usually start with that case at three weeks. Giving the other half a little more time.
Give you bottles a little roll on a table to re-suspend the yeast, and stick them back in the over 70 closet ofr at least another week, or two..and they ALL will be carbed up just fine.
I've never had an issue like that, and I don't stir. I've come to believe that's one of the rationalization new brewers come up with rather than looking at the fact that they simply weren't ready yet.
