Matt - My understanding is that there are two areas on the lake where ongoing dredging occurs: County Ditch #2 which drains into Long Lake from Pike Lake and the lagoon area after the trestle bridge on Rice Creek.
Ramsey County is responsible for dredging Ditch #2. They're supposed to do it every 5 years, but it's usually longer than that.
I believe RCWD has been responsible for dredging the lagoon area where sediment tend to build up.
Otherwise, I'm not aware of any precedent for dredging the channel between to bays or other problem shallow areas. Perhaps Leon could chime in on the channel.