I think that i've got a solution for you.
On Spark Ableton device (not on Arturia VST User Interface), click on configure button.
Next open Arturia VST User Interface
Then click on Loop Mode Switch (on Spark Midi controller or Spark VST UI) and Loop Mode parameter appears on Spark Device.
Go on with turning Divide encoder and Move encoder to make them appear on Spark Device too.
No need to activate Spark Public or Private Input in Ableton settings.
Now when you use encoders for loop divide in Record mode with automarion arm switch enabled
in Live 9, Ableton record all your encoders move.
Just tell me if it works for you.