OK I see about not editing.
16:9 is perfectly acceptable within the +RW format specifications, but whether a particular recorder implements it is another matter. Unfortunately the GX3 offers a drastically cut-down version of +RW.
As I said, to get 16:9 playback in a recording made on the Sony, you would have to rip the title from the disc and edit the IFO file using a PC drive. If you want to get into that I can provide a link.