See it in action here.
This setup works without any circuits or bots. After finishing producing the U-235 it is put on the inner lane of the inner loop. After reaching the left part of the loop it is put on the outer lane of the inner loop. Here Centrifuges get another chance to grab it. If the U-235 is able to finish this second loop it is transported to the bottom left underground. The resulting U-238 gets delivered to the outer lane of the outer belt where it gets prioritized to prevent backing up. Any gaps in the inner lane of the outer belt will be filled by the input belt at the top right. (It's fine to have some U-235 from the Uranium Processing in the input as well)
This setup scales quite nicely and works even with a single Centrifuge. It's also quite straight-forward to increase the size of the two loops.