There are forum members who are experts in aeration. There are Vertex brand aerator knowledgeable folks who may see this post and be able to chime in.

This study was done by Vertex:

Aeration controls midges...

You are lucky in that sense that your lake is private and has a managing association so you should be able to share the costs of setting up aeration stations around the lake with the association owners.

Every lake association that I know of that could get folks to agree to put money towards aeration rather than chemicals found multiple benefits (less dredging, less muck, less detritus and leaves, clearer water, less fish kills from unexpected turnover events, and sandier bottomed beachfronts.)

In the long run probably way cheaper than chemicals especially if you run the lines yourself and already have multiple places where you can provide power to a network of small aeration stations.