I think this is the troubling paragraph:
If, during the course of your period of work in “The Establishment”, you believe that you may have developed commercially exploitable technology please inform your supervisor, the “The Establishment” Director or local Technology Transfer Office (as applicable).
Alice is aware of work that is commercially exploitable in the situation you describe above. No qualifications are given, in this statement, as to when the work is performed or on whose equipment. In my non-lawyer opinion the Establishment would own rights to all work and patent applications mentioned in the scenario above. In fact if all work was begun after month 3, the Establishment might be able to prove that Alice was aware of these projects prior to the celebration, and thus they own a stake in them.
So I would either change the agreement and have the results reviewed by Alice's own lawyer; or, forget the paper. It is a lot of work for something that will likely mean nothing to the profitability of these ventures.