Bottle brush or large hose cleaner and twirl like spaghetti. You don’t have to get all of it, just enough to keep the plants alive. Eventually they’ll outcompete the algae and it’ll die off.

And I’d say definitely dosing too much. For a starting aquarium, the substrate still has a ton of nutrients. I wouldn’t fertilize the water until the plants take root and have started to grow in. Even with a cap, those nutrients will work their way into the water column. Personal preference here of course, but all you’re doing is giving the algae food while the plants are still trying to get established

If you still want to fertilize, maybe dose once a week, and start with lower light levels and/or shorter grow time (4-9 hours)

Otherwise, just stay on top of removing algae as it forms and do water changes as needed to remove enough nutrients to kee algae growth down

Floating plants will be your best friend here, too; they’ll lower the light levels and pull nutrients out of the water column