I don’t think that would be the best approach as the mechanism is strongly related to post objects and not admin screens at all. The plugin mainly needs to set a user ID value somewhere when the screen is requested. If a value is set, don’t allow others besides the ID user to see the screen. A transient is a good place to store values as they expire after a time period.
There are several UI improvements possible through Ajax calls, but simply locking out everyone but the one user will do the job, albeit a bit crudely.
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