Congratulations, Nathan! It's almost right: the last part must be "Amo trans la vivo" (you'd better use the article here).
Esperanto only uses the objective termination "-n" after a preposition when the context implies motion: "Li estis en la Äardeno, kaj kuris en la domon" (He was in the garden and ran into the house).
In Esperanto, unless there is a motion sense, the object either takes the "-n" termination or is introduced by a preposition. In the case of the man who bites the big dog, there isn't any preposition at all, so the "-n" termination is mandatory. Got it now?