Before you make any permanent changes, re-visit the position of the neck. In theory, playing with the neck off-center can affect how the upper octave pad seals (because the upper octave ring may contact that little post the sticks up to work the upper octave arm). However, not in all cases. Some upper octave rings are shaped so there is a wide range of neck-positions possible before contact is made.
This is easy enough to check yourself. If the upper octave pad remains on the upper octave vent without breaking the seal while the neck is in your favorite position, then there should be no problem and you won’t need to make and external changes on the horn. DAVE