Not the answer you want to hear, but a mature, fertile lake in NC is going to support lots of something that utilizes photosynthesis. Your problem is made much worse by the middle of the pond only being 6' deep. Sunlight is probably reaching the bottom of the entire pond for most of the year.

Chemical treatments will knock back the aquatic rooted plants and/or the algae, but the nutrients will remain in the pond - so you will face the exact same battle in the very near future.

Heavy aeration can slightly reduce some of the build-up on the bottom of the pond, IF a significant percentage is organic material (as opposed to silt) and you get some substantial bottom agitation to get the organic muck up into the oxygenated water column.

You might have a cheaper solution than dredging, but it will be ugly - so I don't know which way the HOA would prefer. That option would be to drain the lake, breach the dam, and push the silt through the breach. Or perhaps have an excavator deepen the middle and spread the spoils up higher in the pond so that they may dry.

It is not as simple as it sounds, since up to 6' of muck will NOT initially be workable by a dozer, so you may have several scrape/dry episodes (over the course of a year?) to achieve the depth you want. You also need some place to spread the spoils so they will dry, and can then be subsequently moved or built into a berm.

Just throwing out some ideas for you to chew on. Hopefully, some experts will chime in with some more specific advice.

Good luck on your big restoration project!