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Another approach would be to create milestones for all the end dates you've negotiated, and lock their start dates. (Since they're zero-duration, this effectively locks their end dates too.) Then create Finish->Start dependencies from all the tasks needed by a given date to the corresponding milestone. That way, if something else in the schedule forces a task to finish later than the milestone it's linked to, OmniPlan will display a red violation badge and walk you through correcting the problem.

This is probably the better approach, and will cooperate better with the leveling algorithm.