Nice root pic GPS. I've attached a pic of the roots I got on one cycle in my recirculating deep water culture prototype system. By the way, when I type "FAD," I'm using short hand for "flood and drain" - who doesn't love an acronym.
There is actually a pretty large body of academic literature on three topics relevant to this thread: root restriction (e.g. container), root-shoot proportional growth, and root pruning experiments. Regarding the latter, I believe the typical finding is that roots recover quickly from trimming.
For a more popular hydro story on root pruning experiments, you can read J. Benton Jones Jr.'s article
The Root Whisperer (Maximum Yield, August 2011) where he states:
For most plants it has been demonstrated that just one actively functioning root is capable of supplying most, if not all, of its essential nutrient elements...In general, there is no consistent positive correlation between root mass and plant growth and product yield. In fact, a large root mass may actually be detrimental to plant growth and product yield due to the amount of carbohydrates and oxygen necessary to sustain the function of such large roots.
I'd say that most of my previous pruning experiments agree with Dr. Jones' statements. I've just never tried to grow larger plants in tubes because smaller plants can clog tubes pretty easily - lettuce roots ain't no slouch so to speak - and, taking my cue from large commercial growers, I usually grow larger plants in drip systems. But you never know unless you try, and try I shall.