Besides, that's only if the unpacking goes smoothly and we finish by Sunday morning.

Literal

Besides unpacking [subj-が] smoothly go-[and-て], Sunday [gen-の] morning [until-までで] if-finish [gen-の] talk [also-だし].

それに 'besides / moreover' is the additive discourse marker. 順調に 'smoothly' is the adverbial form of 順調 '(going) smoothly / on course.' 終わったらの話 'the talk (only) if X happens' is an idiomatic frame for hedging — literally 'the story contingent on X finishing.' ~し (reason stacking) appended to the whole, marking this as one more reason alongside others.