Growing system for root crops

After looking at several online reports of methods to grow carrots (which are similar to salsify) I'm not seeing anything that appears to produce carrots at optimal size. This suggests that I may need to devise something different...

In all the videos I've seen so far, the resulting carrots seemed stunted, to various degrees, by the confinements of the growing system. If the carrot is confined within a net cup, it seems to grow in cramped shapes, and if it grows in constant contact with the wet container wall, they seem to be partially rotten when harvested.

I need to investigate more videos and articles to see if this trend is consistent. And if so, I'll need to come up with a system that doesn't constrain the roots and doesn't leave them in contact with the side walls. My first thoughts are either a misting aeroponic system or an alteration to standard Kratky.

Misting might not work well, because (at least in the case of carrots) the crop seems to suffer if the roots are exposed to light.

The kra videos I've seen seem to indicate that roots getting tangled early in the growth cycle may have compromised the final size.

Of course, there's no guarantee that salsify will share the same complications, so I'll try the standard Kratky tank first and see what happens.