Agree about the filter cleaning, just rinse out the media in old tank water and don't worry about that water having algae in it. I would skim the siphon over the gravel to pick up large debris but don't disturb the gravel and the bacteria on it.
How much light is over the tank? How much biological filtration does the tank have? Is the tank planted and how are you feeding the plants?
Once an algal plague gets started it isn't always easy to stop it. Besides the diatom filter some use UV filters.
Your tank is quite heavily stocked with big fish with good appetites. I suspect too much waste for your filter to handle. You may need more filtration. Planted tanks can need more water movement and biological filtration than one would think. You could try submerging house plant cuttings or bare rooted plants at the back of the tank in planters or in an HOB filter to boost nutrient export especially if the tank isn't heavily planted and brightly lit.
My very first monster attack of green water was over a decade ago. I couldn't see an inch into the tank. Reading APD I learned that my bright CO2 enriched tank might also need more nitrogen and phosphorus than fish poop provides. I very gingerly dosed the tank with 1/2 tsp of potassium nitrate and each day the tank was much clearer. It was completely clear in 4 days. Alas in recent years that hasn't helped - been dosing KNO4 already. I was worried about so much as pulling up a group of stem plants for fear of triggering a tiny ammonia surge that would start GW up again. The bioballs in the sump didn't seem to help and they were removed as a nuisance. Later I bought big sponges and I cannot believe the change. I haven't had a single GW episode since and I have taken the tank apart and put it back together several times. Last time the water was sparkling clear within an hour of the pumps going back on. So for my bright tank I need to be sure there is enough food for the plants and a very good biological filter.