tl; dr The launcher is now only under the effect of true polymorph how magic jug is over.
return to the ends of the original caster's body magic jug.
The original body of the magic jar caster is true polymorph while your soul is not in it because of magic jug. His soul later returns to his body ending magic jug or when magic jug ends
… returning to your living body (and ending the spell) …
In any case, magic jug It is no longer a consideration as it is over.
The result is the same as the launcher that uses True Polymorph itself
The added annoyance of the effects of magic jug are irrelevant as magic jug it ends when the caster returns to his original body.