Therefore, my best theory runs as follows: when Madeline and Mitch got married, Madeline had a child from her first marriage in tow. Mitch, either through sheer pride or because he and Madeline were both keen to leave their lower-class pasts behind, refused to raise another man's child in his house, but promised to provide for the kid as long as s/he was raised by someone else. When the kid grew up and found out that they'd been abandoned by their mother and step-father so that they could pursue their image as a "perfect" wealthy family, they developed the hatred for Boston's social elite that led them to commit the killings. At some point Madeline and Mitch discovered the connection and covered up the killings - Mitch out of guilt after realising how his actions had twisted a child he should have accepted as his own, Madeline to protect the family's reputation (judging by their later actions, this seems like the likely set of motivations).
This would also mean that the killer is a little older than Garrett - maybe early-to-mid-twenties when the majority of the murders took place - which fits the profile much more neatly than any of the Hawthorne siblings, who were all in their early-to-late teens at the time of the first murder, perhaps slightly too young to have believably overpowered grown adults. Admittedly one clue it doesn't cover is Mitch's DNA being found on the belt, as he would be the only member of the Hawthorne clan not blood related to the killer. However, it would entirely make sense for the killer to have the belt, as passing off a ruined but still new and expensive piece of clothing to a secret, unwanted fifth child - instead of giving it to charity as they claimed - seems entirely in-keeping with Madeline and Mitch's treatment of this theoretical kid thus far, and would be exactly the sort of vaguely insulting act of condescending kindness that would have led to them developing their hatred for their wealthy family in the first place.