FAS has this to say:

Centrifugation was tried, but the technology needed to spin a rotor at an appropriate speed was not then practical on an industrial scale. The aerodynamic separation processes developed in Germany and South Africa did not exist during World War II; neither, of course did laser isotope separation or plasma separation.

The FAS is a nonprofit which claims to be founded by Manhattan Project scientists.

Bill Wilcox (Oak Ridge's official historian) mentions it in the Voices of the Manhattan Project, but I don't remember how far into the video it is, and it is quite long, but he corroborates this account.

The Zippe-type (a very common model) centrifuge was developed in the USSR by a team of Germans, but (IIRC) Zippe didn't bring it into the West until the fifties.

I found your answer! I'm making another top level because I think this deserves it.

It was a two factors. First off, before the Zippe centrifuge, gas diffusion was simply more economical. Second, the project used Beams-type centrifuges, which were unreliable for them.

This type of centrifuge had a layer of oil which did not allow heat flow into the gas, as such heat flow stopped the separation (the ultracentrifuge you mentioned has that problem). That was an improvement since it worked at all, but weight on the bearing combined with friction around the oil gland broke down the centrifuge. Zippe's design had neither thrust bearings nor oil gland - no extra weight, no problematic friction.

At the time, the technology to separate the two isotopes didn't exist yet, and they had better results with a different process, developed originally in the 1930's by the Joliot-Curies.

Source: A Brief History of Science, by Thomas Crump.