Has your well water been tested? You may have an abundance of phosphates in it which will encourage algae growth. Ultimately, you have an imbalance in water chemistry...withdrawing light is not a long term solution and probably won't work.
There are phosphorus-absorbing products if excess is the case. You might also want to consider a UV sterilizer in-line with the Eheim output.

Green water won't hurt the fish, but is unsightly and the only permanent cure I know of is a balance of beneficial, algae eating bacteria and for that, I honestly don't think you can beat sponge filters, or as already suggested, a UV, but that's not a cheap solution.

I'm currently wintering a bunch of young Wakin goldies in a 125 in my greenhouse and last week, made the awful mistake of getting overambitious in cleaning the double sponge filter. I should have cleaned only one and left the other and am now paying for my folly with green water, an issue that won't be corrected until the sponges are again well loaded.

BTW, for a 125gal tank, what are you using to diffuse your CO2. I have a more modest 58 gal but have been dissatisfied with 1) ceramic disc diffuser, 2) bubbling into eheim intake, 3) red sea reactor 500. I am going to try the Aquamedic Reactor 1000 but it is a lot more hardware--at least it is external though.

some additional info

Here is a link that might be useful: Aquarium Algae info

Green water happens a lot in newley planted aquariums. Some people say that a black out will help, and some don't think it will. If you try a black out, you need to make sure that there is no light coming in through a nearby window. Plus in the long run, if you tank is by a window you will always have algae problems. A black out will not hurt the fish, it will stress your plants, but they probably won't die.
Adding more plants and keeping your fertilizers in check should help. The key is to get your plants growing at a rate that will use up all the nutrients, before the algae gets them. This is what you want anyway, healthy fast growing plants. Sometimes when you add bright light the plants try to grow, but if they do not have the proper fertilizers they can't grow, and the new leaves will look almost see through. You need to get your plants to out grow the algae. Green water dosen't occur that much in established tanks, except in some cases after medicating for velvet or other fungus infections.
I agree that if anything you are adding to your tank contains phosphates, you will get lots of algae. I would not think that turning your aquarium light off mid day is a good idea especially if your Co2 is on a timer with the lights. This is when you need it the most! With planted aquariums, you need to produce an environment that is as close to natural as you can. And turning the sun off in mid afternoon is not very natural. If anything your lights should be their brightest at mid day. 12 hours of lights on won't help with the algae either. 10 hours max is the best to keep the green stuff under control. Do some research, you'll figure it out. You shouldn't have this problem again once your tank is established. Good luck!

Buy daphnia off ebay (I do not personaly sell any) and put them in the tank. Put your fish in a breader (they eat daphnia very very fast) and turn off your filter till the water is clear. This may take up to a few days to a week.

What I did was buy a 5 gal tank and bread the daphnia till I had thousands and then put them in the aquarium. The water was crystal clear in 2 days. It took about a week to go from a few hundred to a thousand daphnia. If you have metals in your water (copper, lead, iron...) daphnia wont live.
On ebay (I have no affilation, just a happy customer) I bought from dallasdiscus two times. He ships fast and mails out at the begining of the week.