I am very confident that your problems are not due to your skimmer. I have run ASM skimmers, and I know what they are capable of. I have a G5 running on a 225 gallon system maintenance tank, and while it produces lots of skimmate, it can barely keep up. So a G6 on more than 300 or 400 gallons isn't going to be too much.
In my experience, the best growth occurs in systems that have strong lighting, heavy nutrient import (by way of lots of feeding), and heavy nutrient export (by way of a big skimmer). A tank with low nutrient import won't grow well even in the absence of a skimmer. A tank with insufficient export will grow well for a while and then taper of significantly because of increasing nutrient levels. You have to find the right balance.
I would look to other aspects of your system. The first thing I would do is check and then double check your water parameters. Unless they are within acceptable ranges, you won't be successful no matter what you do. Watch for temp fluctuations of more than 1.5 - 2 degrees. Test your salinity often and be sure that your top off procedures are keeping the fluctuations nearly undetectable. Look for steady ph throughout a 24 hour period (no more than a .4 swing). Make sure your nitrates are less than 3 or 4ppm. Run a phosphate reactor if you can't accurately test for phosphates (most test kits will always tell you that you are phosphate free, even when phosphates are high enough to be problematic.) Monitor your calicum, magnesium, and alkalinity. A big deficiency or excess could be causing problems. For all of the trace elements that you can't test for, make sure you are doing regular water changes (anything less than 50 gallons is barely worth doing with a tank as large as yours.)
Once your water quality is taken care of, start looking at your flow and lighting. Since your tank is very tall and you are only using four 250 watt bulbs, you are not pounding the tank with light by any means. For really intense lighting you need more than 250 halides of tanks taller than 25 inches, which yours is way in excess of. I think you will find that your growth is slow in the bottom half of the tank regardless of other factors. Your flow is likely also deficient just because the tank is so large. Ideally you would want in excess of 40X turnover. That means your pumps need to be putting out 24,000 gph. That's equal to 8 Tunze 6101s.
Brad