Okay, I snapped a few quick and dirty (figuratively speaking) photos of my bag mod, and you can see that it's so simple, it's laughable.
I used a bag that I already had, which I was not using for anything else; it's a cheap bag from WalMart which cost me about $6US. I am looking for an inexpensive water bottle carrier that I can attach to it, or I may wind up buying another bag that has a water bottle carrier built-in.
Here is the bag sitting on my workbench:
I mounted it on a piece of scrap board I had lying around for front and rear views. Note: The board is only 13" wide, somewhat narrower than a typical tray table, but the belt of the fanny pack can easily and quickly adjust to fit pretty much any tray table, or the back of a car seat, or anything else in that general size range.
Front view:
Rear view:
Profile view:
As you can probably see from the photos, all I had to do was to cut a length of 2-sided Velcro to the proper length (I used 22"), and feed it through the hanger loop that was already on my fanny pack:
The Velcro goes up over the top of the tray table, runs down the back, and loops around the belt, which keeps the bag from sliding down the tray table. Since the top loop is Velcro, I can adjust it to any length, and raise or lower the bag till it's at the height I desire.
It's also very simple and easy to take off, so I can lower the tray table any time I wish.