I'm not an expert, but based on what I've read the water itself cannot be radioactive, rather it's suspended particles that emit radiation. Remove the particles and the water becomes safe, or at the very least a whole lot more safe than it was.

Distillation might be the safest bet.

One of my thoughts is flocculating might be helpful. I've been researching it lately, and from what I read of some backpackers it can possibly be as simple as getting some alum from the store, stirring and letting it settle correctly, and then pouring the water off. It seems like it'd remove stuff that normal filters don't, as I've been researching it with regards to expedient fluoride filtration--carbon does not remove fluoride from water, but flocculants do. I'm not familiar with all the reasoning behind this but it might be something to look in to with regards to removing radioactive ions.

I'd still probably want to distill it if at all possible. I'm eager to hear others' thoughts on this matter.