Interestingly enough, Ars Technica is reporting today that NASA pegged the cost of meeting this timeline at $35B (https://arstechnica.com/science/2020/02/nasa-p

Interestingly enough, Ars Technica is reporting today that NASA pegged the cost of meeting this timeline at $35B (https://arstechnica.com/science/2020/02/nasa-puts-a-price-on-a-2024-moon-landing-35-billion/ https://arstechnica.com/science/2020/02/nasa-puts-a-price-on...) so your estimate of the cost of a Manhattan Project and my suggestion that it was that order of magnitude seem to both be correct!