Your numbers are fine, within the assumptions you make, which is a marginally competent customer who actually wants the thing built correctly.
Problem is, some of the biggest factors in the disaster were that HHS kept changing the regulations and requirements, provided no realistic statement of work or concept of operations, and proactively suppressed necessary technical detail to avoid any “leaks” of it to program critics.
So, your team would still have failed. Just a lot less spectacularly, most likely.
I have a 9 month requirements-nailing-down phase (see the thread body for that). In the contract, I would build in the clause that they have 9 months to work with us to have a Business Requirement and a Tech Spec put together. Fail, and we get paid and walk from the project.