We have a death record, an obit, and a gravestone for Max Bloom Max Rosenberg Bloom , but nothing to conclusively tie him to the Vermont family (nor rule him out). His death record gives his parents as Jacob and Bertha Tobey (which may be 2 first names rather than a first and last name). His gravestone names his father as Yaakov Yehuda. The obit mentions no siblings.
However, if Max Bloom was really born between 1857-1864 as various records indicate, and Toba was really born in 1804, then we have a probable age problem. While it's not strictly impossible that Toba could have given birth to a child at age 53, such occurrences are exceptionally rare.
So it's likely that Toba's birth year is incorrect, and/or Max's birth year is incorrect, and/or Max Bloom is not the same as Max Rosenberg son of Jacob Yehuda Rosenberg and Toba Fine.
(Similarly, Zorach's birth year is given as 1859. This is probably not the birth year of Zorach-son-of-Jacob Yehuda Rosenberg and Toba Fine, though it may be the birth year of some other Samuel or Zorach or James Rosenberg or Rozaitsky.)
I notice also that the siblings' birth places are widely disparate; Simon is alleged to have been born in Pinsk, while Isaac was alleged to have been born in Kovno. While people did move around, so we can't rule out the possibility, it seems more likely that the birthplace for one or the other of these siblings is incorrect.
Max Bloom of Chicago was from Jurbarkas, which was in Kovno Guberniya, as noted on his arrival manifest (under the name Mordche Blum).