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For tasks which are completed ahead of schedule...
1) Set completion to 100%
2) Adjust end dates into the past (somewhat optional)
3) Level the project, and check the box saying "Don't schedule any task before date" and choosing the current date and time.

Yes, leveling will "double-book" you, but only if you've got a task with an end date in the future that's already completed. Which isn't really double-booking, because you've already gotten one of those two things done. It's intentionally ignoring that completed task, because it knows you won't really be doing it tomorrow -- you've already done it.

The important part is to use the check box, so that leveling doesn't move incomplete work into the past.