Been staying until the end and the re-que starts before leaving. Now 3 runs have NOT counted towards the needed 35 for the title... gear/weapons don't drop at the end, pages don't convert and the daily quests don't complete either... thought Bungie fixed this 2x already...
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Have you tried only going in through the map? Had the same issue and it would only count if I chose to go through the map instead of the table in the tower.