If you can cover about half the surface with floating plants they will do several things for you:
1) Nutrient uptake. Reduce the nutrients that algae need and the algae will grow slower.
2) Shade the pond. Reduce the sun that algae need and the algae will grow slower.
At some point, the conditions will not favor the algae, and the UV may not even be needed.
Other plants can help:
Below the surface will probably get shaded out the same as the algae. Put these in there if you have a cheap source, but assume they will die.
Marginal plants, in containers around the edges, tucked into the rocks as the pond/stream spills... Plants with their leaves in the air will grow best, because they get their CO2 from the air. They are great at nutrient export, and some will help shade their little area of the water.
Are there fish in all parts of the water? Golds and Koi can destroy the plants. Some pond keepers have a separate living filter system where the water is pumped through a stream that is planted. I have seen designs where the 'stream' is a trough-like construction, and the plants kept in containers like hydroponics. Looked REALLY NICE. The exterior was some sort of stained wood, matching the deck and bench. Really showy plants were growing in it. Mine is more of a cobbled stream flowing though a peat bog. Also looks really lush while the plants are growing (some go dormant). Another way to exclude the fish from part of the area is to build an island. Depending on how high the island is (it might not even reach the water surface) plant with marginal plants.