I'm the one who brought up the Booth family to begin with. As for Tweed, he should still hopefully run Tammany Hall and the New York political machine. So long as there is no Thomas Nast it gives him potential to control the patronage of one of the largest cities in the continent and to decide elections.
Sorry, I didn't see that. Ya, Tweed will probably be part (or already is part) of the Albany Regency and Van Buren's political machine. Under them, New York is pretty much kept 100% Crown (with a few exceptions) and it'll probably stay that way in the foreseeable future.