It's a wonderful strop.
I've done some thinking and research, guys, and the only thing that keeps coming back is what I saw in this video:
YouTube - how to use an automatic stropper
That's the only explanation (weak though it be) that I can think for the strop's design.
Also, to counteract the deficiencies in my own eyesight with regards to where the strop-leather ended and the handles began, I decided to polish off the patina on the strop, to make it easier for me to see what I was doing. Careful application of fine sandpaper yielded the following results...
http://i12.photobucket.com/albums/a2...roppolish3.jpg
...as opposed to this sorry sight, earlier today...
http://i12.photobucket.com/albums/a2...ophanging5.jpg