I've worked on a number of projects where bill rate is something like $250-$400/hr per engineer depending on complexity, access to source code, size of the project, etc.
Usually equating to something like 10-12k for a single engineer on a project for a week. For bigger projects like this I would think it's totally reasonable to see anything from 4 engineering weeks -> 12 engineering weeks depending on different pieces and especially given this is a very high profile project. Based on that estimate of something between ~40k-120k. I know that's a huge range, but just wanted to share what I do know.