Good info here in this thread.
I would not dose unless you test, and yes, skimmers will remove trace elements from the water. The more powerful the skimmer, the more they can remove. The good that they do, however, in removing disolved organics far outweights the bad by removing trace elements and you should be doing PWC
anyway which fixes this problem.
Maybe, in very heavily stocked systems dosing would be needed, but then again, I would not do it without a test kit.
The sunlight has caused me this problem in the past. WAY back in the day when I was running a 55 with perfecto lights I got a huge green algae problem when I moved my tank too close to a window. I figured it was the house window because the algae grew the most heavily on the single pane of glass facing that window. I got the same problem from a 39gallon mirror back tank once, the mirror on the back of the tank grew algae from perfecto lights like a lab culture. If I forgot to clean it once a week it blocked the light from the mirror, the algae died off, and the tank crashed. Now that mirror back is a fresh water tank.
I would test your tank for everything possible that could cause algae issues, make sure nothing is out of wack first, just so that you don't do something dumb and make it worse by mistake.
If all checks out ok, I would guess that you are just going to have to scrape a lot. Some snails do a better job than others at getting algae off the glass. I like cearth (sp?) snails the best for this. No amount of snails will ever get it all, however. Part of the fun of keeping these things i guess.