I do think massive amounts of more troops would have made a difference if we were looking to really control the country with military force. I remember as a BCT XO in April 2003 in Tikrit trying to balance early Coin ops with raids, and with trying to secure all of the ammo dumps around; we simply did not have enough troops to do it all.
If I may ask sir, what was your BCT raiding? Were you going after FRLs? When elements of the 4ID came into zone vicinity of Samarra, Apaches went to work engaging targets across the the highway from an entire battalion coil (which I was a part of); "targets" in an area we'd already cleared and have control over. There was a lot of ordnance and weapons around in Tikrit when TF Tripoli moved south, but by the time we pulled out we had already established a pretty brisk trade in cigarettes and orange drink.

I'll have to disagree with you about COIN in April 2003. It wasn't happening. Sure, military leaders were trying to talk with Iraqi leaders and figure out whether we needed to be talking to mayors, sheiks, or some incarnation in-between, but we were also installing ourselves as "mayors" of sorts, and were all to quick to write PAO stories about it (which may have fueled our problems).

There's been substantial Bremer-beating concerning the disbandment of the military (and I don't want to belabor that here), but if we had been doing it with, by, and through Iraqis back then, does the large numbers hypothesis still hold true?

if it was the additional brigades under the Surge practicing so-called new coin tactics that lowered violence in the latter half of 2007 and if the majority of those brigades continuing to practice their so called new methods are still in place, then how do you explain the recent increase in violence not only in the south but in Baghdad?

I don't think we were screwed up in Iraq until 2007. I think we were simply screwed up in pockets, and those pockets served as areas (or seams/gaps if you will) where our enemy was able to get into our loop, build his center of gravity, and drive us to swat the fly with the proverbial hammer. We were not unifromly screwed up across the entire country.

As for explaining the current spate of violence, if you cull through my previous posts on the SWC, I believe that we did not surge enough in Baghdad (I was thinking a deliberate clear and hold through the city requiring several divisions), that we needed to square ourselves with Sadr, and that Iraq was only on a low simmer when we rolled into summer 2007. Come elections in the US, the violence would pick up for sure. Maybe that is coming true, but I don't know.

The assumption to Dr Kilkullen's thinking is that good Coin methods underpinned by sound theoretical thinking can replace mass of troops on the ground.
Perhaps you and I read Kilcullen differently sir, but I don't see him as actually having this sort of underpinning in his work. I think he believes that lower numbers of troops, actively practicing COIN and not wrapping themselves in too many force protection pillows, and working through the folks who really know that turf, are going to get you to your endstate faster than plodding around en masse.

I think he recognizes there is a time and place for large formations, but if they aren't being employed properly, the are just shooting our strategy in the foot. We did not have the aptitude, temperance, nor patience to do a good job in 2003-2005, regardless of how many boots we had on the ground. Tie this problem to the woefull reconstruction efforts during that period, and I can totally agree with you that the military was not in control of things in Iraq. Like John T. Fishel said, no matter of troops would have mattered with a crappy strategy.