The sentence is ambiguous but the second meaning ("we all want to save them") is not likely to be right so I would rule out a mistranslation.

If that were intended, we could say:

Nous tous, on veut les sauver.

To convey "we want to save them all" in everyday speech, I believe « nous voulons les sauver tous » / « on veut les sauver tous » would be preferred to « nous voulons tous les sauver » / « on veut tous les sauver » but the latter form is far from unheard, e.g.:

et les desserts… il nous faudra revenir encore pour venir à bout de l’ardoise car nous en avons goûté quelques-uns mais on veut tous les manger !!! (trip advisor)

With a singular subject, tous is no longer ambiguous:

Je veux tous les tuer. RTBF. I want to kill them all.

Hence, your first hypothesis is right: it is perfectly fine either way. As iNyar commented, prepending tous emphasizes it. The order could also have been chosen for the reasons you cite (poetry/rhyme).