Thanks for the advice, everyone!
I have been watering with chlorinated "city water". My usual practice is to load my truck tanks in the evening, and then leave early in the morning to water the trees. That gives the water a little time to outgas the chlorine. However, my water needs have gone up greatly due to my additional tree plantings plus the drought at our farm. I must utilize my supplemental water supply at the farm to save time and gas money, but the system definitely needs some tweaking.
Preppers use bleach in their water supplies and the water remains potable to humans. However, bleach is an effective herbicide.
The most efficient lake algaecides are frequently copper based. Yet copper sulfate is the active ingredient in the products that kill the tree roots in sewer lines. Fortunately, some of these algaecides are marked as safe for irrigation water.
"The dose makes the poison."
It appears that my best option will probably be to mix my chemicals at very low rates and see if they can be effective below the recommended treatment concentrations. If not, then I will slowly walk up my concentration.
I also believe getting the tarps on my distribution tanks should be a priority - since there are no negative side effects to denying light to the algae.