The split happened with a greek translation in the ancient era,
The Encyclopedia Judaica (1971), says:
"Originally a single unit, the Septuagint and the Vulgate divide the book in two, titling the resulting parts First and Second Kingdoms (1 and 11 Samuel), followed by Third and Fourth Kingdoms (I and II Kings). In the later Vulgate tradition “Kingdoms” becomes “Kings.” [my comment- in early non-jewish bibles, you had no "samuels," instead 1st Kings, 2nd Kings, 3rd Kings, 4th Kings] Hebrew manuscripts continued to treat Samuel as one book until the introduction of the printed Bible in the 15th century, when the division into I and II Samuel was accepted."
According to the Jewish Encyclopedia 1901, the split entered Jewish books because:
"it passed into the editions of the Hebrew Bible published by Daniel Bomberg in Venice in the sixteenth century."
("1st and 2nd Kings" are also only 1 book just called "Kings" (מלכים-Melechim) in the Jewish Mesorah.)
The bonus question is exactly right, all the numberings have similar origins.
Adding 31 like you say would be a way to do it, but you also have to consider that not everyone would know what you are referring to and it would not serve much purpose as the chapter and verse designations have a similar origin.
Instead you could describe the area you are referring to, for example, "In Shmuel, in the event of David joining with the Philistines..." This is similar to how Torah portions are. However most people would have to search for sometime to find the correct area.
If the Jewish corpus wanted to as a whole, they could standardize portions of Nach (the Writings and the Prophets) like the weekly torah portions, and then everyone would easily know where you are referring to, but I don't see the standard chapter and verse scheme going anywhere.