ghdmd, let's back up just a bit here first.. The more water you want to move, the finer the bubble size needs to be. Although there is some oxygen transfer, the main source of raising O2 levels is exposing bottom water to the surface-THEN O2 from the atmosphere is absorbed into the upper layer, so max flow is key.
#2, aeration will not reduce algae, please understand that, I don't care what is advertised, aeration does NOT stop algae.
There are 2 basic means of getting rid of algae. #1 is manually removing it. #2 is "something else" has to use the nutrients before it forms an algal growth, such as aquatic vegetation.
First thing to do is figure out the nutrient source and get that fixed by limiting that source.
When you decide you need aeration for pond health and want to go solar, let's talk about that because using an inverter consumes even more energy that you need to provide and store.

EDIT: I went and read the links you provided and in the example they show 2 6v batts for a 12v system which is really not near enough, you'll be using welding cable to keep the efficiency up.