Correct me if I have the details wrong.
72G tank.
Well stocked with fish, about 26" worth, mostly cichlids.
You've got about 72 watts of lighting via 1 10,000K tube plus 1 actinic tube. These are T8s?
Running for about 6 weeks.
Sounds like your water changes are no bigger than 10 gallons at a time, 13%?
Did not notice what your water change schedule is if you mentioned it. What is it? 10 gallons a week? Every second day?
You said you're only feeding spirulina. How much and how often? Spirulina should not cause algae issues, not any more so than any other food.
In the future, if you could provide all relevant information in your first post this will ensure that you can receive more accurate help much quicker, instead of people trying to pry the details out of you for three pages.
I conclude any combination of three possibilities.
1. In my experience a bit of diatom growth is normal in newly setup aquariums no matter how old the silicone is or how brief the interval between setups was.
2. Lighting may not necessarily be too high but it may be high enough to promote an excess of algae growth. Unless you have a lot of plants to soak up the light and nutrients, algae's the only thing it can fuel. The actinic light may be exacerbating the diatom growth, I've heard actinic lighting in freshwater setups can cause algae problems.
3. Your nitrate test may simply be wrong. Unless you're doing a 50% water change a week which as far as I can tell you aren't, you seemed surprised and unenthusiastic at the prospect of doing a water change of this size, I would expect your nitrate level to be much higher.
I would start doing a 50% water change with gravel vac once a week. I would test your nitrate test kit against someone else's, personal preference but I'd swap the actinic tube for another 10,000K tube or a 6500K, and with that much light you may as well plant some vallisneria in there.