While I was away dealing with Real Life (TM) Thorne has answered most of this better than I could, but since I had the answer in my head, I'll dump it anyway...
I don't know if I have failed to explain my point clearly, or if you're simply dodging it. I'll try to make it more clear.
The basic theory of AGW is not based on a "complicated formula": it's a simple statistical relationship, and anyone with Statistics 101 can do the math and see if the results fit the theory. The data you need are atmospheric CO2, which is the same everywhere, and average global temperature, which you get from the public records of weather stations in a suitable number of locations around the world. You don't want just one, because it may not be representative (for example, the UK has been warming up over the past decades like most places, but it lags behind the global average because of the well documented weakening of the Gulf Stream,) but you don't want an impossible number; fifty or a hundred chosen at random should give a good first approximation.
None of this is hidden or difficult. One reason the vast majority of climatologists have come around to AGW is that it's so easy for them or someone they know to replicate the experiment and find it gives the same answer. It doesn't take a global conspiracy to make people believe what they can see for themselves.
The complicated fomulae come in when you try to give policy makers useful advice on what to expect year on year and country by country. Averages are not much help here, because everyone acknowledges that the effects will be very different from place to place; so we get into the field of long range weather forecasting, with all the uncertainties that this implies. BUT - and this is the important point - none of this complication affects the overall global picture, and none of the questions about it affect the fact of global AGW. Even if it were to be proved - which it certainly isn't so far - that one centre had commited outright fraud in their modeling, that would have no more bearing on the truth of AGW than the fact that the movie "Day After Tomorrow" is rubbish science.
Let me explain another way. There is a river called the Severn with a dramatically powerful tidal surge, and for decades people have been arguing over plans for a tidal power project there. Trying to predict the effect of the project on the tidal and current patterns calls for complex models and masses of data, and it wouldn't surprise me if people on both sides of the controversy had tweaked their models to predict what they want. BUT, whatever the accuracy of these models, the tide will rise and fall: the tide is a fact regardless of how its local effects are expressed or predicted. Likewise, AGW is a demonstrated fact regardless of how accurately its detailed effects have been modelled.
Since the actual recorded temperatures have been rising for decades, I guess this is about cycles again.
Perhaps many people have come to the same conclusion but why then are these same people simply pooh-poohing the downward trend of temperatures in recent history?
Every climatologist knows about climate cycles: they've been studying them for most of a century, which is why they get so annoyed when people suggest that it's a new fact that changes everything. And as you say, the long term trend up till the last century was that the world is in a cooling phase, which is why people are so worried about the fact that the actual global temperature has been going up when the cycles should be pushing it down. It means that if we haven't got a grip on global warming by the time the cycles trough out and go into a warming phase, we'll be in real trouble.