In your second sentence you say that the tasks have ALAP date constraints because the project is scheduled to an end date. In your third sentence you say “The exhibition task has a must start on constraint date”. However, you do not need to impose either of these constraints (a set date for the event is not sufficient reason). If you do impose the date constraints then you have abandoned the critical path method, and since it is your best friend in project planning this is not a great idea. If you simply list the tasks and link them as predecessors/successors, and don’t impose date constraints at all, the earliest possible finish date for the project, the date your event can occur, will be revealed by the network model. As long as this date is earlier than the target date, you know that the project can be achieved, that is, you know it is feasible, and you can measure the feasibility by the float on each task, and the difference between your target date and the earliest date.
What you want PROJECT to do for you is not possible because it cannot make the decisions that only you can make.