Ik heb hier 'southward' gebruikt, maar dat werd niet goedgekeurd...
you can't say "to the southward" as southward is an adverb so it must say something about a verb or an adjective
And if you just say '... going southward'?
yes that's possible, I'm going southward. But then you'll need a subject (as a verb needs a subject). But that was't asked to be translated. So it's possible to say, but can't be used as translation of this sentence.