If you go back a few pages and find the wiki file on algae lighting requirements, you'll see that the sun emits 80,000 lux and algae grows best in 2,500 to 10,000 lux, and photoinhibition sets in at 15,000 lux. As far as the CFLs being too close, the anecdotal evicdence in and of itself does not suggest either way that heat or intensity is the cause of hindered algae growth when the lamps are too close. However, when you consider that
1) algae grows better in warm water than in cold water
2) HP LEDs have been shown to 'burn' the algae
3) the wiki article regarding intensity
4) water cascading over the algae will keep it at relatively the same temperature regardless of proximity of light source (within reason)
then photoinhibition due to high light intensity due to close proximity of the light source becomes a more probable cause of low algae growth. You have to remember that intensity is an inverse square function. If you have the CFLs 4 inches away, then move them 2 inches closer, by halving the distance you quadruple the intensity. So it is true that the photons don't care how far away they are from the screen, but the algae cares how concentrated the photons are. So I agree with you that CFLs cannot generate the intensity of natural sunlight. But we only want 1/8 of sunlight at a maximum, and with a lower output source in such close proximity you actually can get it too intense for what the algae likes.
This is the significant difference between growing plants and growing algae. This application of light to grow algae is very specific, you will not easily find another application which requires the light source to be so close. We deal with a set of rather unique and unusual rules with the ATS, so you have to be careful when making comparisons that other factors are taken into consideration. There are general guidelines that are somewhat flexible, which makes it great because many designs will work just fine, but there are also more firm guidelines that cannot be exceeded without resulting in a significant loss of function. To this point, the modern aquarium ATS is very much an infant in this regard IMO, because no one has taken the time to do a truly scientific study of the effect of each component of the system as a whole. What we have right now is a quite a bit of real-world results that have produced a general design that is highly effective. Finding all the 'sweet spots' would probably increase efficiency a little bit, but probably not enough to justify spending thousands of dollars just to figure out how to get 5% more growth. But it would be nice to know the exact rates of growth given a set of conditions, so that you can size an ATS perfectly, and so that you know, for instance, exactly how much load one square inch of screen can handle. So far, that guideline is based on real-world experimentation that has proven to be true. End of rant!!!
The bottom line here is that you don't want the lights too close. I'm not saying that absolutely this is your problem. I'm just trying to use a process of elimination to help determine the issue with your tank.
If all thing were going fine over a long period of time (same lights & lighting schedule, same feeding schedule, same corals, same fish, etc) and then you cut out the skimmer and added the ATS, and the skimmer wasn't actually skimming, then you might have had a drop in O2 that caused an algae outbreak. However, like I said before, it looks like you have plenty of flow in the tank with 2 power heads, and low O2 exchange just seems less likely. If this happened very recently, then you may consider snow melt runoff. In Iowa, when the snow melts and all that salt and grime gets pushed down the system to the water treatment plant, our water quality goes through the floor. It happens every year. Our LFS in fact does a very large PWC on their 600 gallon tank every year right before the snow starts melting, and then leave the tank alone for about 2-3 months. They do this because one year they lost almost everything in the tank due to water contamination, even after filtering the water with and RO/DI system. I have actually had the exact same issue in one of my tanks. My RO/DI read 0 TDS, but even after switching my carbon and DI beads, the 'pure' water read 0.09 on my Hanna Phosphate photometer. I had provided 10g of topoff that had something in it that caused a nutrient spike and dino outbreak, and I almost lost 4-5 corals.
A long term stability followed by an outbreak of algae and diatoms after removal of an oxygenating skimmer sounds like a good explanation, I'm just trying to think if there could be any other cause. Generally, any change in the system will cause a new set-point, and that's why I suggest that, if at all possible, you get the ATS established before pulling any equipment out. I guess at this point you could add the skimmer back in to see if that eliminates the algae in the DT and raises the pH back up, and wait untl the ATS matures to remove it again.