I might read the label on Sonar to see if it will hurt the trees.
SONAR isn't likely to have any impact on trees (besides saplings that have their feet "wet") - but it also won't have any affect on FA since it is a herbicide.
Algaecides shouldn't have any affect on your trees. However, controlling FA without also impacting the phytoplankton might prove challenging.
The judicious use of Cutrine Plus Granular within shallow areas that represent nurseries for FA (before the FA detaches from the bottom and migrates with wind) might be a viable option.