Instead of starting a raid timer when you turn in the quest to get your end reward, why not start the raid timer as soon as the raid completes?
This has two benefits:
1) players will no longer have to wait an extra 3 days if they happen to forget to get their turn-in reward.
2) at least some of the recurring exploits that allow people to bypass raid timers would be eliminated by this change.
Starting the timer on quest completion is how Epic quests work, so it shouldn't be too difficult to make raids work that way too.