Edit: it really is bizarre because Radon is primarily produced by reactions underground/in the earth and has a relatively short half life (3.5 days). I don’t see how it could be atmospherically sourced without it being a hazard to the whole community, regardless of the bizarre convection currents that bring it into your house. It’s unlikely to be produced in your attic.
If I were you, I’d want to know more and understand how this is all happening lest you raze and rebuild and find you still have a problem.
I would suspect fly ash as a possible source if the house ever had a coal-burning furnace. Or maybe someone had a watch-painting operation or mixed radioactive glazes or paints there. Someone with appropriate equipment could do a much better job identifying the source.
Any notion of whether it's β or ɣ radiation you're detecting?
Demolition is going to need careful monitoring to ensure you don't contaminate the entire site.