Hiring 200 more people would just make it 2 or 3 years late, not just 1 year late.
Keep the client informed of the progress. Springing a surprise like this on the client on the originally planned delivery date, without any warnings well in advance, should count as proof of poor project management and make the software company liable for a significant chunk of the costs. The client shouldn't have to swallow that cost if they were kept in the dark.