shawn, sorry to hear about the damage to your lychees. are you pugging to try to improve chance of recovery or because you want to alter the shape/canopy of the tree? my gut feeling from killing a bunch of lychees in the past is to not do anything and hope it comes back.
i know pugging has been mentioned in posts before, but i don't recall if anyone has actually done it before and reported back.
i've caused a number of lychees to defoliate to almost 100%. they always bounce back except when it happened in the late fall when the tree was going into dormancy.
i'll note that when they lost all their leaves, i don't recall them having growth below the first bifurcation. these were medium size trees, (trunk 2-3 cm diameter) though
edit: added photo of mauritius