more stem plants in the tanks should help to outcompete the algae for the access nutrients.
Yeah, plant it heavier. Throw some water wisteria or some other fast growing plant in it to absorb the excess nutrients
That was my 1st thought too. You don't mention what cap you have over the dirt?
If you read every thread on Dirted tank problems you start to see some common points. Lack of frequent water changes (you on that one), Gravel vs. Sand caps, and lightly planted tanks or moderate planting with slow growing plants.
I think the Sand preforms a function in that there is a think "seal" of the finest sand that sits on the dirt. I belie that slows down the nutrient flow into the water column in a way that gravel just can not do. I'm unaware of any natural body of water were gravel pebbles sit directly on dirt.
Even with sand you need to keep the nutrients in the water column in balance. Plant mass & water changes address that.
I feel the biggest error people make is focusing too much on the parts and not enough on the tank as a whole.
Before you spend $$ on substrate and do a tear down, I would suggest add as much Hornwort as you can. Let it grow to 2" thick on the top of your tank. Then as you get in balance remove it gradually.
Going to a sand Cap, 2" of dirt 1" of sand works well. In the long run it will be a simpler system.