Far enough that any alternatives identified still have time to be prepared, which usually means many months rather than weeks before the constraining date. Reconstructing the record alone can take a while, and any option that depends on building new facts needs considerably longer.
Let the weakest dependency set the date
The schedule is driven by whichever input takes longest: retrieving old passports, obtaining records from a former assignment, or waiting on a decision the employer has not yet made about the role. Identify that dependency first and count backwards. Leave room for the possibility that the advice is that the assignment ends, since that outcome also needs lead time to manage.
There is a further reason not to leave this late that has nothing to do with the analysis. If the advice is that the assignment ends, the organisation has to plan a handover, the household has to plan a return, and both take months. Treating the constraining date as a deadline for a decision rather than for a departure gives everyone room to manage it properly.
Set the review far enough ahead that a negative answer is still a manageable one, and diarise it rather than relying on someone noticing that a date is approaching.