I think you're right about the root development in the raft system.
you could try filling your 5 gallon bucket with sand and running either a drip system or ebb n flo system to provide the nutrients.
Alternatively, you could just fill it with dirt and keep it watered.

Thanks Grizzman, i like the idea of using sand and a drip system. I will have to give this a shot.

I will need a bigger light. Right now i am just using flourecent T-8 daylight bulbs for my lettuce.

I tired horse radish last year in sand. It rotted. Not to say yours will though.

This year I bought some of the expanded clay balls and put about 3" in the bottom, added the roots, and then covered them with more of the same. I made sure the water level is way below the 3" mark as the grow rocks will wick water up, and the roots in water will cause rot.

A good friend of mine grew both horseradish and potatoes last year in Perlite. He put 3" of perlite in the bottom of a tub with small holes in the bottom. He then put in the "tubers" covered in more perlite. To water he took the tub lid and put it under the tub, and used it like a saucer. Basically he would put water in the saucer (lid) the Perlite would wick the water up to the roots, and they grew nice.

Just some ideas.