Well, you got the wrong property here. outside-staff-priority tells how to stack outside-staff objects with one another. What you need here is \override CueVoice.TupletBracket.staff-padding = ##f to stop TupletBracket from being shy of the staff itself, never mind other outside-staff objects.
Got it - thanks! So, Werner, this should be the solution you were looking for? Lukas