Okay, I have a process for you to try. I got it to work, but I didn't have my
selection perfect and I didn't want to start over so...

- Open the round image.
- Zoom in at least 400%
- Using the lasso selection tool, select the pixels on the right edge. I think
you will want to be just inside the very outside pixels, as it looks like
there's a dark halo. Also, you'll want to be careful to avoid the highlight.
This is going to be the tedious part of the job.
- - Get the best selection you can.
- - You can hold down the shift key and select to add more pixels to the
selection.
- - If you want to remove pixels from the selection, use Select>Select
Inverse, hold down the select key and add to that inverse selection. Then
inverse the selection again.
Once you have a good selection, save the file so you save the selection.

Now, copy and paste the selection, and move the new object away from the round
image. (Maybe put it on its own layer and lock the round image.) Copy and paste
again, then use the arrow keys to move the second pasted item over so it
overlaps, but doesn't show any transparent pixels in between. Repeat until you
have covered a good-sized area.

At this point, one thing you could do is group the shapes, copy them to a new
image, and then crop a rectangular area. Export this as a .png to flatten, but
not distort the colors. Open the flattened .png and then you can resize the
shape wider and maybe apply a motion blur (Filters>Blur>Motion Blur..., set
direction to 0).

Then, you can repeat the fun with the other side!

Other than the care in making the original selection, which is something you
can tweak, I think these steps are fairly simple. Good luck!