Purgatory is supposed to be a place where people go in preparation for Heaven, a place of cleansing.
There was a lot of killing on the island, so I don’t think the island was Purgatory.
The characters were better behaved in the alternate timeline (ATL). And a lot of issues were settled in the ATL. And there was a lot of healing in the ATL.
One of the most telling scenes was between Jack and Locke. In the alternate timeline, after Locke gains “awareness” (in the recovery room after surgery), he told Jack that he didn’t have a son. So I think what you said “I think Jack’s son David was a way for Jack to resolve his issues with Christian” makes a lot of sense.
But then there’s the scene with the plane wreckage at the end...
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to my Catholic brain purgatory is the place you go because you’re not good enough for heaven “yet”....you get there eventually....and those that are pretty good people but not perfect get there faster than the ones who are only a little good.....such is my recollection of St. James grade school....