I agree with you for what causing the string sounding off shape especially the dirt and oxide as you can notice the Elixir last much longer.
Do you leave the strings tight after each play.
I think everyone leaves their bass tuned up to pitch when not playing. Putting your bass in a case may help dust from getting into the strings, but most importantly, you need to wash your hands before playing - every time. Roundwound strings should last at least a couple months if you wash your hands.