How are you supposed to store for Uranium Ore for transportation if the containment building is locked behind the building requiring promethium science while it only requires utility science?

You must process the uranium immediately (use belt)

I'm at a similar point in my playthrough where I'm currently automating uranium. Uranium ore and uranium-235/238 explode when I put them into chests. This means I can't use logistic chests. I don't think it's realistic to restrict uranium to belts only. You could remove the explosions from uranium and keep it for radioactive waste. Another idea would be adding a new item, chests (including logistic chests) that serve as early containment units and are capable of holding uranium.