On my current map I have 381,000 depeleted uranium in my logistics network. That doesn't count the dozens and dozens of warehouses full that I've shotgunned to get rid of it.

Is there a process I'm missing where I could re-process it and get something useful? Or should I just keep shotgunning the crap out of it?

You can use depleted uranium to make plutonium. Plutonium and plain uranium can be used to make nuclear fuel without enriching the uranium first, so that process effectively consumes depleted uranium and plain uranium (i.e., basic processed ore) to make fuel, getting rid of your leftover depleted uranium in the process.