So from my experience, you can only get the Spindle for completing the Daily ONCE. That is, if you have an account with 3 characters, you can only get the Spindle when it's the Daily Story mission once per account. I'm guessing it goes the same for the Vienna Singer (exclusive ship), you can possibly get the ship for completing the Lost to Light mission on the first go when the Legendary Marks are available. Can anyone confirm this?
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i have done this quest on all characters and rerun 30+ times, no ship. i hope this is a bug. bungie did reply to someone about this in the help section