That's helpful! Sorry to hear about your fish - those are hard lessons. Knowing the size of the pond is critical if you are using chemicals. But the goal here will be to avoid all chemicals, so then you can just guess! haha!
Remember that the algae is telling you something about your pond - you have an excess of nutrients which you can address in several ways. The first is to get more plants growing in the pond, which you said you are working on so that's good. The second is to make sure you aren't overfeeding your fish - less is better when you are facing green water. And I would say your pond is fully stocked with your nine koi - in fact, you might be close to overstocked.
In the meantime accept that new ponds are green - and be happy about that, because that algae is helping to keep the water healthy for your fish. Barley straw is kind of a yes-no thing; yes it is known to release hydrogen peroxide as it decays, but no because now you have another source of organic material in your pond which is what algae feeds off of. The better approach is just to use hydrogen peroxide directly - just the plain old brown bottle drug store variety kind. It will kill string algae and may help with the green water.
But again - remember that when you kill algae you end up with - you guessed it - dead algae in your pond... more organic material to feed the growth of more algae. Algae Fix is not really a permanent fix - you'll be married to it forever if you depend on it to clear green water. So try not to chase the symptom and instead work on the cure. More plants, less food, lots of aeration and patience.
The WH and WL would help, but they may be struggling in the heat. Some people find that taking them out of the pond and putting them in a bucket with a little Miracle Gro for a few days can help perk them back up.
Have you posted photos of your pond here? We'd love to see it!