The 3/16" plate is appropriate for the boxing plates, and boxing the whole frame can be done but is not mandatory.
What you might think about doing in your "C" notch is to weld in the "C", add a doubler plate over the "C" that welds to the top and bottom plate of the frame, and then box it in. The box really only needs to extend 10"-12" forward and rearward of the "C" if you are not fully boxing the frame. Typically the boxing plate will be long enough to catch a crossmember that can be used for an upper shock mount as well.
Any other boxing plates need only to be installed where you are adding a crossmember or where you are sectioning the frame. More than that is just a whole lot of work for very little structural gain and more weight. I would probably section the frame in the area that a crossmember will attach to just for additional strength.
Adding an "X" brace in the center of your frame adds much more torsional stiffness than lateral crossmembers alone, and they can be built to accept the rear transmission mount.