1st off, the radon is harmfull like chlorine to your respitory system when you are in the shower. Yes the radon eventually fills the carbon, but, lets for example sake compare it to chlorine, the filter I mentioned will reduce it for 150,000 gallons to less than .01 PPM(parts per million). Then change your filter, and your safe for another 150,000 gallons.
Reverse osmosis I have in my kitchen for drinking water availability. What you are doing is compressing water through a filter membrane, that only allows in Hydrogen, and Oxygen particles. Everything else present can not get in. It wastes alot of water, for example a good system will use about 6-8 gallons of water, to produce 1 pure gallon of R/O water. You can pick up a whole house R/O system, for about 4 grand, plus the filters need to be changed every 3 months and cost about $250 each time. Just a kitchen sink unit would cost about 200 for a decent R/o system, and filters about 50 bucks each time you change.
Like I said, I would be MOST comncerned w/ the steam when you shower giving off radon gas into your lungs. Art the very least put the Big Blue filters on I spoke of. I have piuctures of my set up, if you want pm me your email, and I'll send them to you, along w/ the cheapest places i found for the filters, and initial hardware to.