In one piece I read, Groves and Oppenheimer got in a panic when they realized they couldn't get enough U-235 or get it pure enough. So that is when Oppenhiemer decided to test use all the various purification methods in a series building up to the electromagnetic separation as the last step.
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Yes, that's right.
In my opinion, the definitive history of the Manhattan Project is Richard Rhodes' "The Making of the Atomic Bomb" which recounts the very situation you describe -
This is the book that introduced me to Szilard, Fermi, Bethe, Oppenheimer, Groves and so on.
It's quite detailed and doesn't shy away from discussing intricately complex physics right alongside political and moral issues.
A very compelling work.
.d.
--------- "If human beings had more of a sene of humor, things might have turned out differently."
Stanislav Lem