Similar to "Es heißt", "Ich heiße euch", "Ich heiße es", "mir ist", "mich wundert" this construction can be seen as having a recipiect in the front and the actor in the back.
Zuhause war der Himmel Blau.
No doubt "Himmel" is the subject, but "Zuhause" is the theme. Comparing similarly "Mir war das Glück hold", "Das Glück war mir Hold", this seems to be a clear case. Your variant is inadmissable, "* Mir das Glück war hold" is not grammatical in modern usage, and at best reminds of archaic phrases (for which I have no example at hand).
The original phrase using "Und kaum zuhause angekommen" is interesting in its own right, but hardly matters here. Indeed, *Zuhause angekommen war der Himmel ..." would sound as if the sky had arrived. This can be seen in a transformation analoguous to "Glück above". "* Der Himmel war kaum zuhause angekommen blau". Of course, personal genitive pronouns bind stronger, and move differently than adverbs of place, let alone participles, so the example is a bit contrived. This does not impede the verdict. Arguments from transformation have little relevance overall.
Adding Und in front magically changes the expression into a formulaic verse with a zero-pronoun. We can imagine that Und draws it in from the context. I will also note that und in this place very much reminds of end-lich. While "Ende zuhause angekommen" sounds odd, the semantics are reasonable.
I will also note that auxiliary "haben" could be left out in some archaic construction (Nathan der Weise "Wer hat je gehört, dass Saladin ... bestraft" [Todo: link]), and that English "has come, has arrived" indicate that this could have been the case in a precursor of this formular.