Yes, Manchin and Sinema are more problematic. Still, I don't think you addressed my actual point, which is that removing the filibuster to pass federal abortion protection would be a big deal, and the best the Democrats could hope for today is a 50/50 vote with the VP breaking the tie. I'd personally be astonished if they even tried, not because they didn't feel like it but because it would very likely be a gun that blew up in their hand.
I believe this is the kind of issue where you'd have to overcome the filibuster, not remove it. This isn't something Democrats were realistically able to do in 2008-2010, and they definitely can't do it now.
No, I don't think it's nitpicking I think it is factually wrong (except that, yes, Sanders and King are Independents). Not only does King vote with the Dems on most important votes, he's not even the most centrist or least loyal to the caucus member of the Democratic Caucus; In the current session, on key issues, if the caucus fails to gather the majority it needs (which usually means there is no vote: Schumer is pretty consistent about that), it is usually Manchin (D-WV) and /or Sinema (D-AZ) — more often the former — that is the problem. (And both of them are to King’s right by both current session and career voting history.)