Rutherford took over in a Business Coup of doubtful legal force, and got away with it, by being a bully I would guess.
Many who had followed Russell, and still called themselves Bible Students left, especially after the 1925 debacle, about which Rutherford admitted " I made a bit of an ass of myself didn't I ?". ( I think he meant arse).
The followers of Rutherford were not much greater in number than the Bible Students when Rutherford strove to distance himself from them, and further from Russell, by instituting a new name.
His successor, Knorr, followed the methods of Corporate America, and drove the business model to success, via profitable printing and selling of literature, and making money from Conventions.
If Rutherford and Knorr had not been so interested in $$$ and more interested in really being a Christian Org. the JW's would probably not number many at all today.
With regard to your points in the O.P. the line you trace is more accurate and truthful than what I saw in the WT mag a few years ago where they traced back through Russell and then selected religious figures during the intervening Centuries until they got back to the 1st Century, a most spurious Line of Succession and History indeed !