Rule 704.3 on checking state-based actions states, in part:
[...] If any state-based actions are performed as a result of a check, the check is repeated; otherwise all triggered abilities that are waiting to be put on the stack are put on the stack, then the check is repeated. Once no more state-based actions have been performed as the result of a check and no triggered abilities are waiting to be put on the stack, the appropriate player gets priority.
Based on the wording "if any state-based actions are performed", this implies to me that if no state-based actions are performed because they are replaced, the check would not be repeated and the player could get priority. This is supported by the famous rule 614.6:
614.16 If an event is replaced, it never happens. A modified event occurs instead, which may in turn trigger abilities.
Suppose that Alice, while at 4 life, controls The Great Henge and two Exquisite Archangels. Her opponent controls a Balefire Liege, a Void Maw, and a Quakebringer that was dealt 4 damage earlier in the turn. On Alice's turn, something simultaneously deals 4 damage to her and 4 damage to Balefire Liege.
State-based actions are checked, and two such actions would be performed: Alice would lose the game for having 0 or less life (704.5a), and Balefire Liege would die from damage ≥ toughness (704.5g). One of Alice's Exquisite Archangels replaces the former, exiling itself and attempting to reset Alice's life total, but this is prevented by Quakebringer (119.5). Void Maw replaces the latter, causing Balefire Liege to be exiled instead of die.
Because no state-based actions have been performed as a result of the check, the "otherwise" clause kicks in. Assume that no triggered abilities trigger as a result of any of this. State-based actions are checked once again, and now it is Alice's second Exquisite Archangel that fails to reset her life total and is exiled. Additionally, Quakebringer, which was being kept alive only by Balefire Liege's +1/+1 buff to red creatures, has been dealt lethal damage and would die, but is exiled by Void Maw instead. Again, my understanding is that none of this counts as a state-based action being performed.
Now that no state-based actions have been performed and no triggered abilities are waiting to be put on the stack, Alice gets priority while having 0 life. The instant she passes priority as a result of casting spells or activating abilities, state-based actions will be rechecked and she will lose. But since mana abilities do not reset priority (117.3c), she can now tap The Great Henge to gain 2 life and save herself.
Is this analysis correct? Or perhaps I am correct in the core idea, but this scenario does not allow for it?