I think Richard Marklew’s method is probably the best options in terms of accuracy. You should be able to get exact curves with curve tools. However, if you want a quick’n’easy not so accurate method, use proportionate editing (the doughnut icon at the bottom of the 3D view window in EDIT mode) to pull up edges while rolling the wheel to maintain 3D proportions. If you get a dent in the curve, you should be able to fix it by rotation of the bend area. There should also be X-axis symmetry options so you only have to do one side.
Edit: Why don’t you work the other way? I mean, why not duplicate the curved mesh you’re wanting to end up like and perform simple edits (edgeloop add / delete etc) to get it how you want? Also, why are your pieces all one mesh? It would be easier to manipulate them as units if they were separated.