Green away is just going to make dead algae that will still need to be filtered out. I seriously would start filtering the water manually with cotton batting. Find some way (even if it has to be a temporary line from the filer to the pond) to run the pond water through a small basket or something that can hold the cotton fill batting in place while the hose from the filter runs the pond water through it. I know it sounds crazy but it works VERY well! In 24 hours you will see a dramatic difference and in just days you'll see the bottom

After the pond is clear, use the fountain to put batting in, less likely to be seen, to keep the pond clear of single cell algae. Unfortunately because your pond is in the sun most the day, this will be a never ending battle. The good thing is, Batting is a very cheap, and I have even been known to buy stuffed animals at the thrift store and use the stuffing out if these, that way I can just throw away what gets nasty and its even cheaper

Lillies and floating plants will help shade a bit but the fish like to eat them so there is that problem lol
oh and welcome!