It's a toss-up right now, depends on the traffic. 324 generally hits Windsor before 6am, so you'd be looking at shots south of there in any kind of light, the return trip, 323, would likely leave Brattleboro at dusk or later.
Burlington to Rutland should be at least 5x a week if not daily, I believe they're north out of Rutland in the early hours, back by the afternoon.
Rutland to BF should be out of the yard around 9ish, that may be your best bet. I believe that is most, if not all weekdays, they may or not be running a train during the weekend.
Avatar: NHV 669 at the south end of the "Pompy" in White River Jct., VT on 4/29/1993. Photo by Richard Roberg.