This month, the SFWMD should update us on the updated plan that WDW submitted. I expect the plan to be approved, which could lead to Disney's announcement of a closure date for the Rivers of America at any point after. If the plan isn't approved for some reason, that would push things back.
I view the original information I was told as outdated at this point with the plan yet to be approved by the state, but if I had to guess when we will see Tom Sawyer Island and the Rivers of America close, I'd say by after Easter at the latest. Just to be clear, that is my guess, not inside info.