The big problem to public access to totally private waters that exist as a private utility or government property is the liability issue. What the state legislature needs to do is to pass a very comprehensive Public Doctrine law that absolves private utilities, private corporations, non-profit organizations (land trusts, etc.) and state and local governments from any kind of liability for allowing the use of their properties for the public good (recreation, fishing, hunting, hiking, etc.)
These laws would be similar to the laws protecting landowners when a hunter/landowner both sign the Consent to Hunt form. The process would probably require getting a permit like you do for fishing the Saugatuck Reservoir, the NYC reservoirs, etc. or hunting on some of the utility properties like the CL&P lands.
The state could use a "carrot & stick" approach of providing some tax relief for those organizations that step up to allowing public access (the carrot) or if they don't step up, then (the stick) in the form of a tax assessment for the taking of public resources from the Public Doctrine resource portfolio. So they would pay a tax surcharge or penalty, even for a non-profit organization, if they disallow public access.
That would be my Bill if I were an elected member of the state house or senate.