A 10 gallon hood would probably fit but it would be four inches to short so you'd have a gap on either side of a couple of inches. My 20 gallon has java ferns tied to driftwood, a large amazon sword and a small patch of micro swords, an anubias (not sure what variety, probably nana), some anacharis and pennywort planted in the background, some java moss tied to some rocks and floating bunches of hornwort. All are growing, well, like weeds! I run the Current USa LEds about 8 hours a day, dose liquid carbon daily and Flourish and LeafZone weekly.
You're right about the algae and sunlight though if you can control the nutrients by having the plants outcompete the algae, you might get by with it. Still, I think the 10 gallon hood might be an temporary option though it will light the tank unevenly, so center the hood and plant in the middle. You could put java ferns and moss on the edges as they will tolerate less light. Hornwort would do okay floating on the edges as well.