So how rigid is the new FX Crown continuum barrel?

I don't understand the question, what complaints were there about the "old" Crown barrel, presuming you mean the same as the IMPACT with the liner inside a steel tube, inside the shroud?

If as your thread title says you are asking about the "SUPERLITE" system which is on the Crown Continuum then can I ask what exactly are you worried about?, the liner itself is held extremely rigidly in the rear nut, which then uses the same barrel stub as the old system to locate into the action, albeit with 4 screws on the sides of the action rather than two on the top.

This concept makes it possible, to not only not to have to remove the barrel whilst leaving the scope in place, but has a huge weight saving WITHOUT reducing stiffness, as the shroud itself effectively becomes the stiffening system, hence the 700mm barrel can now be used in the Crown Continuum without having to worry about droop from a long heavy barrel.

I hope that makes sense, I have both the old and new Crowns and do not find any difference (or reduction) in accuraccy in the new SUPERLITE system.