I see several potential problems.
Is that bulb fluorescent or incandescent? If it's fluorescent, you have decent lighting for low, possibly up to medium light plants. If it's incandescent, switch to a spiral CFL bulb in the 6500K spectrum.
You said it yourself. Get a timer. A cheap timer from the hardware store will do. Twelve hours is the maximum time I'd leave your lights on.
Just so you know, amazon swords will get way too big for your tank. I have two that are busting out of my 29g at the moment. You're correct about them being heavy root feeders. I don't think they draw a lot of nutrition from the water. If they're all you have left, stick to the root tabs and stop the Flourish. You're just feeding the algae.
Proper nutrition is the way to maintain a planted tank. Light counts as a nutrient. My 29g has major algae problems, but that's because I have an ill-fitting hood, an AC70 that off-gases my inadequate DIY CO2 system, and low intensity light in the wrong spectrum that gets partially blocked by the mineral-etched glass in the hood. I have to scrape the glass once a month and BBA runs rampant. My swords love root tabs and I just started using Flourish, but it seems to accelerate the algae issues.
My 20L has a tightly fitting VersaTop with an AC30 and an AC50, a DIY CO2 system, 36W of CFLs and 36W of T5s. The only spot I have algae issues is directly under the CFLs. I'm going to switch from my "warm white" (I think 3900K) CFLS to some 6500K CFLs and see if it makes a difference. I also dose this tank with Flourish.