The framers expected their Constitution to prevent the formation of factions in Congress...
I think the opposite is true. They expected a "multiplicity of sects" to protect liberty. Meaning that there would be so many factions that, as James Madison put it, "For where there is such a variety of sects, there cannot be a majority of any one sect to oppress and persecute the rest."
They quickly realized this wasn't happening, however. So, I think you're largely right about the rest. I think the main problem with the filibuster today is the current version of the rules removed the need to actually hold the floor and keep talking during the filibuster. The actual work involved in holding a filibuster is so low that it is easy to abuse. Restore the need to do actual work to hold up a bill and Senators will be less inclined to use it.