Do you have status with any of the chain hotels in Mumbai? Some statuses come with late check out (say to 4pm or 6pm) as a benefit, and even if not many hotels will be quite generous to their elites.
For that late I'd expect to either check out normally and store bags to collect on way to airport, or pay another day (or half day if they allow it). It is a bit late to expect a free late checkout.
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