First of all welcome to the Forums!
Have the pond shop test for nitrates. A pond in full sun is going to want to create algae. Warm water and bright sunlight create perfect habitat for algae blooms. especially if there is an abundance of nitrate. More water movement may help... Adding a reed bed would certainly help especially if you can pump water from the pond through it on a sort of artificial stream but that requires even more
energy inputs and permies are lazy we stay away from external inputs of energy if we can. ... but before all of that think about what is going in to the pond.
Do you fertilize the
yard at all... are fertilizers running in to the pond when it rains?
Do you
feed the koi/goldfish... How much... do you need to? There may be enough wild sources of food that you can at least cut feeding back.
another thing to think about is adding some more
trees on the south west side to help cut down the sun exposure. Maybe fast growing every greens so you don't have to worry about leafs dropping in the pond.
Plenty of others with pond
experience here so I will let the forums take over more suggestions.