Bumping because I have the same issue. Has anyone managed to complete it after deleting the quest? I'd rather not since I'm at step 5 and would rather not redo that progress, but if it works I might.
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i just deleted the quest because it said I hadn't completed the exo challenge. jSo once I deleted it, I went and picked the quest up again from the abandoned quest box next to the postmaster on the tower. Then Iwent and did the exo challenge again and hey presto, the exo challenge was completed and now I am on the vex finisher stage of the quest. So, one abandoned quest, once repeat exo challenge all good. When I abandoned the quest I did not lose any progress, this is the same for most quests involving weapons.