How many integrators are there?

So, I got an innocuous question the other day from Sarah Seibert, communications coordinator over at PSA: How many security-focused systems integrators are there in the United States? Easy, right? So, I gave a wild-guess response (I was busy, and it didn't seem to be life or death or anything):
"Really hard to say. What's an integrator? When does an alarm company count? Etc. If I were going to ballpark, I would say there are about 25,000 security system installers total, and maybe 8,000 of them do some kind of commercial work, and maybe 1,500 of them are sophisticated integrators with some kind of software engineering capability (and this includes the IT integrators who have become interested in security). That's going by our circulation efforts and industry show attendance. But that could actually be a low estimate. I'd be curious what other people say."
So, I was pretty happy with that. Sounds smart, right? This is what I get back from Sarah:
Thanks for the info, Sam! Here’s what Scott Goldfine said: We estimate about 3,000 of the estimated 12,000-15,000 installing security companies to be legitimate systems integrators. The rest would be more security or alarm dealers.
Well, that's of course unacceptable (and insidious on Sarah's part - ho hum, Scott thinks you're wrong by about 100 percent). One of us has to be a little more right than that! We're thousands away from each other. A full order magnitude away from each other. And neither of us put any rigor into our estimates whatsoever. So here's what I tried by way of putting a little rigor into it. I'm happy to listen to why my analysis sucks, and why you have a better answer:
Okay, I'm not sure about integrators, but here's at least a starting point for security installers: California, the most populous state, has 2,047 licensed alarm companies, which equals one company for every 17,953 people New Jersey, the 11th most populous state, has roughly 1,200 alarm companies according to the NJBFAA, which equals one company for every 7,250 people (or so). If you figure the 9 states in the middle are somewhere in the middle of those two states, and we'll go on the low side at 1,500 per state, you come up with a total of 14,900 alarm companies (or so) for a population of 173,100,000, which equals one alarm company per 11,617 people. If you take that rate of one company per 11,617 people and apply it to the 304,000,000 population of the United States as a whole, you get a total of 26,168 alarm companies for the United States as a whole. I like that number because it makes my guess of 25,000 look smart. Further, if you look at California's numbers, there are 13,423 employees for those 2,047 alarm companies, an average of just 6.5 per company. It seems hard to believe that a true integrator could have fewer than 15-20 employees, so here's some more math: If 50 percent of the companies average 3 employees (true trunk slammers), that would leave just about 10,000 employees for the 1,025 companies remaining (if we're averaging 6.5, it makes sense that half would have about 3 and the other half would have about 10). If 50 percent of those companies average 7 employees (another spot in the middle), that's 6,400 for the remaining 513 (25% of our total) or so, which average about 13, which is getting closer. So, if you go with a quick and dirty estimate that 20 percent of companies have 15 or more employees and thus could likely be expected to do commercial work of some caliber, and you apply that to the national number of 26,168 that gives you a total of 5,233 or so commercially focused companies (loosely categorized as integrators) in the United States. That's at least not a wild guess.
Please note that I would have gotten the exact number of licensed alarm companies from the state of New York but you had to make the request via fax and I simply refuse to use a fax machine for any purpose whatsoever. Whaddaya think?