Slightly cloudy water - plant/CO2 related?

I recently (less than two weeks ago) removed my gravel (and UGF), replaced it with Flourite, planted my tank and installed a DIY CO2 system.
I've changed 25% of the water twice, and polished the tank three times over the past week and a half with a diatom filter to remove dust/algae/debris, and the tank has clouded up soon after each time. I'm assuming that this is a bacterial imbalance, like what happens in new tanks, resulting from the overhaul. I decided to leave it and hope it would resolve on its own, since the chemistry's fine and the fish don't seem disturbed.
this morning it occured to me that it might be something I'm not familar with, and that living in fog might not be great for the plants, so I thought I'd ask for opinions.
Thanks

Okay, I think I may have a problem...
I diatom filtered the tank (again *sigh*) and took a decent look at the filter contents. Green. So what looks like a foggy, smoky haze in the tank may actually be (cue the shower scene music from 'Psycho') Algae!
So is a blackout (the only cure I know for 'green water') the only route to go? My plants have just started taking hold in the tank, I'm worried about what 3-5 days in the dark will do to them.
Is it worth trying anything else (algicides, filtering with the diatom filter every day, huge water changes, severely curtailing the time the light is on for a few days etc.), will waiting for the tank to settle after being overhauled help at all, or should I just go straight to a blackout?
I've heard that a handfull of daphnia (live of course) will clear a tank of unicellular algae in a matter of minutes to hours, but I've never seen live daphnia for sale!
Anyone got a suggestion? All help is appreciated.

I doubt I could afford a UV filter, though that does seem a nice, easy solution...
I've been reading on The Krib about this and (I need to go back to chemistry class) I think I'm starting to grasp the causes of green water.
I've tested my NO3 just now and it's almost zero. Apparantly if your nitrates are zero and you add Nitrogen and Potassium to the water, you cause a favourable chemical change that will help eliminate the green algae. I'm not sure I understand everything I read but I'm going to keep at it and see if I can battle the root chemical imbalance that's causing the problem. While I'm at it I'm going to shorten the length of time my light is on and continue filtering the nasty stuff out, so hopefully the combination will prevent me from having to black out the tank (but if necessary, I'll absolutely do it).

Thanks for the replies, guys.
The problem is with the 45g, the specs are up to date - I try to post any changes as soon as they occur.

Tonight I bought Plant Gro NPK fertilizer - I've been terrified to add any more nutrients to the water for fear that the algae would multiply into a solid green mass that would climb out of the tank and take over my living room... I believe that that's actually backwards, and I need to FEED these plants so they'll out compete the algae - correct? I feel like SUCH a newbie here, I really appreciate all the help. I added a dose of the NPK tonight which brought the NO3 up to 5-7ppm and the PO4 to ~.25. Am I on the right track, thinking this isn't enough and I may need to dose again to get the levels close to twice that?

The plants are actually growing like crazy, everything that was green when I planted it (with the exception of the Cabomba, which is just a brighter, lighter green) is producing red/pink new growth, and the leaves look healthy as far as I can tell (no yellowing, clear spots, dying leaves etc.). The CO2 level is pretty high (30+ mg/L), I'm assuming this is good for the plants (and the fish show no signs of stress) but is this a major factor contributing to my little algae farm? It would be very easy to ease off on the CO2, I've got several bottles chained together and can easily disconnect one if that's wise.

If there are specific levels of nitrate, phosphorus, CO2, pH etc. that I should be aiming for to kill off the algae, please let me know and I'll do my darndest to get this tank balanced.