The easiest way to center the pivot point permanently is by using Tool > Deformation > Unify. This however also resizes your model.
The second option is also easy to perform and will retain the models scale. But it involves a couple of extra steps.
1 ) Set the pivot point with Transform > S. Pivot.
2 ) Store a morph target with Tool > Morph Target > StoreMT.
3 ) Clear the pivot point with Transform > C. Pivot.
4 ) Perform a 100 % morph with the Tool > Morph Target > Morph slider.
You should note that both methods do not ensure a 100% symmetrical model. There may in fact be less symmetry after performing either method so therefore it is advisable to perform Tool > Deformation > Smart Resym on each subdivision level, starting with level 1.