Good stuff Jim. Out of curiosity are the falls the Hoosick with a "K" while the actual river is Hoosic without a "K"?
My understanding is that:
(1) The river is onsistently referred to as the "Hoosic" in all three States through which it flows (i.e., MA, VT and NY).
(2) The mountain range and associated valley (only in MA) is referred to as "Hoosac" - - and one of the local high schools is "Hoosac Valley."
(3) The original name of the Town of Adams (in MA) was "East Hoosuck" (an archaic spelling) - - and you can still see it on the town flag - - although some old maps spell it as "Hoosuc" (without the "K") instead.
(4)The name of the town in NY is "Hoosick Falls" (another archaic spelling) - - and I believe the same is true of the actual waterfall there.
Confused already?
Now on to the bonus round:
There are 3 branches of the Hoosic River: the North, South and Main - - each of which originally had its own name in Algonquin.
The name of the Main Branch was the "Hoosic" (or variants thereof).
The name of the South Branch was the Ashuwillticook - - which is now the name of the bike trail in MA that runs from Lanesboro to Adams.
The name of the North Branch was the Mayunsook - - which is now the name of a farm (and B&B) in Clarksburg, MA.
Sorry if this stuff comes across as pedantic, but I belong to the local historical society, and had to bone up on it years ago, but never really had a chance to "use" it - - so to get my "money's worth" I trot out the whole megillah whenever I can.