The ideas you already have are really good ones.
Another possible approach would be to look at the algae as the result of excess Nitrogen in the water. (That's one of those things I learned in that failed attempt to get a Masters in Environmental Engineering

)
High carbon items such as straw and wood require lots of nitrogen to
compost (errr. decompose). It might be that keeping algae in check is as easy as adding enough wood chips into the water to eat up the nitrogren.