I don't have any experience with reducing my light output, but I know other planted tank keepers will elevate their lights higher above the aquarium either by hanging the light from the ceiling or by making a stand (stacked books on the sides of the light) to increase the distance between the light and the water. Also, anything the light passes through will reduce the amount of light entering the tank, so you can try putting a screen or clear plastic (tupperware?) under your light, but I'm not sure if that can mess with the light frequencies plants require for photosynthesis. I would reduce your photoperiod to 5-6 hours and adjust the high of your light until you find a nice balance.
Luckily, fast growing aquarium plants are usually considered to be weeds and can be super cheep. Water wisteria and any type of elodea/egeria should be really inexpensive and you can just throw them in at the water surface. I know they sell them both at my local petco, and I've heard they're at some petsmarts as well. Any local live fish store should have those plants and will probably sell you clippings for cents - just look them up and call ahead. Duckweed, and parrot's feather are plants you can find at pond stores that will grow at the top of your water line for shade and again are plants that you just need to keep a few leaves or a stem of and they'll grow quickly. Devil's Ivy is one that you might already have in your house, or you can ask to break a short stem with a root nub off at a garden or restaurant and grow it with its leaves out of the water. You can also attach some of your java moss to something floating at the top of your tank. This will allow the moss to grow very rapidly and dampen the light on anything below it. I do this in my tank and it makes a nice little bed close to the surface that my newts spend their nights in. Actually it looks like you have some floating cholla skeleton that would be perfect. Just weave a few strands of java moss through the holes and it will take off. If it gets filled with algae just cut it back.
Keep in mind that any algae growing in a place you don't care about is competing with algae growing in a place you don't want it, so it's a good idea to let grow in areas that are out of sight or on a part of your hardscape that looks neat with a little green.
Ghost shrimp will probably do a wonderful job at keeping algae off of your plants' leaves and are commonly sold as feeder food so they can be just a few cents per shrimp. I saw a huge difference in the amount of algae in my tank after adding some shrimp. Snails are another option, and I would go with either pond snails (usually free), trumpet snails, or ramshorn snails (a nerite snail is probably the best algae eater but too large to clean smaller leaves). Just know that by introducing snails that you'll probably have them forever (excluding the nerite as they can't reproduce in fresh water). It's unlikely that snails will attack your plants unless a leaf is already dying.
I'm not sure if you've had live aquarium plants before, so if you haven't, I want to let you know that it's common for them to 'melt' shortly after taking them home and planting them. This is very common in anubias plants because many growers start them in a terrestrial set up so the leaves they have are too waxy and not useful one submerged. Don't give up on your plants and throw them away if the leaves start degrading, just be patient and it's likely that they'll grow back. It's harder keeping a planted tank with newts algae free because water flow, fertilizers, and small (edible) algae eating invertebrates really help, but as your plants establish they'll need less maintenance.
