This is an anamorphic project? Meaning, the viewer in Final Cut shows a 16:9 image and not a letterboxed one?
For exporting, use the ‘Quicktime Conversion’ setting and then manually change the frame size to something 16:9. I suggest 480×270.
As for tape, it’s quite possible that it IS going to tape correctly. And by that I mean it’s putting a squeezed image that fills the 4:3 frame. It’s very possible that the GL1 knows it’s anamorphic and is thus SHOWING it as letterboxed on the viewscreen so that the picture looks correct. In other words, it might be the camera viewfinder that’s making the letterbox.
When you play the GL1 tape out to a TV with an analog cable, what happens? Is there a menu setting to change the aspect ratio on the analog output? What happens when you do that?