Your fish are dying from a bacterial disease called Slime Disease and/or a parasitic infection which mimics the symptoms of Slime Disease.
What I recommend be done to treat this is start off by changing 20% of the water in the pond. Then add pond salt to the water at a ratio of 1 lb per every 80 gallons of water. This is a particularily high dose that will eliminate parasites but not harm the fish.
Once the above has been done begin to treat with a medicine called TetraPond Pond Fish Treatment which is a wide spectrum medicine. Click on link below for a view and description of the product which is sold at most major pet stores and online. Once adding the initial treatment leave it in the water as is with the salt. After one week has passed add another dosage. Before adding the second dosage do another 20% partial water change. Do not add any salt when doing the second water change.
The combination of the partial water changes, addition of salt and the use of the TetraPond treatment should fix the problem in your pond.
Yes the salt might harm or even kill some of the plants but it basically comes down to the plants surviving or giving the fish a chance to survive.
Thank you for your accept and bonus and please let me know if you have any questions.
Hi again and sorry for my delay in getting back to you.
I can certainly understand your predicament having a pond of this size so instead of using the TetraPond Treatment use a medicine called Potassium Permanganate which is found at some pet stores, hardware stores and online. Click on link below for an overview of the medicine.
If you decide to use this medicine you'll be able to save on the expense of using/adding pond salt as it won't be necessary.
Be very careful when doing Potassium Permanganate as it's potent stuff. Make sure to carefully follow the directions on the product label before dosing.