> How did we end up with the word with the long-o having one o, and the word with the short-o having two?

Neither is pronounced with a long "O" sound or a short "O" sound, and they both have the same vowel sound. (A long "O" would be the vowel sound in "lone", for example. Short "O" is like "log".) The difference is that you use your vocal chords to pronounce the "S" in "lose", making it an English "Z" sound.