I'm going to say it's long because it is the last syllable in the word, receives the ictus and is followed by the principal caesura.
sorry but I don't understand your point at all.
-ta being the last syllable of the word explains nothing, and I see no obvious reason why it should receive the ictus.
In all the metrical commentaries I've ever read, accents and grammar have never been used to justify quantity.
accents and grammar don't justify quantity but they give us a hint what the quantity of a vowel (and hence, in some cases, of a syllable) might be if this is not obvious at first glance.
in our case, the accent on the third syllable from the end (a/sparta) clearly shows that the word should have a short last syllable, otherwise such an accentuation would not be possible.
also, knowing that all the neuter stems get a short -a in nom., acc. and voc. plural is not justifying the quantity. it's rather the other way round, actually: quantity comes with the flexion, it's a part of the flexional ending.