I attached the nylon webbing strap as I described and then used my Nashbar bike cover as the keep-clean wrapper. I laid the cover on the floor, upside down and opened it, placed the folded bike in the center, pulled the near and far sides up and tied them under the webbing strap like gardeners tie the corners of a tarp to hold a pile of leaves, pulled the front and back ends of the cover toward each other and under the webbing, tucked one end through the other end's loop of Velcro and down to the yellow Velcro loop, where I secured that black loop, then tucked in the loose baggy sides into various crannies of the bike. I think it will pass muster and is easy to do. This bike cover is very light but made of strong waterproof nylon fabric, not as heavy as the Nashbar bike bag since it's not intended to carry the bike's weight, just to cover it. It comes with it's own little tote bag. I'm going to replace the webbing strap with one that doesn't have such heavy steel hooks, just loops or knotted loops I tie. When I pick it up, I can either use the strap as a handle or as a shoulder strap. I can feel and grab the bike rack, seat, etc., for more secure handling. This wrapper provides a clean outside, not protection against damage, but that's all that is required for carryon. If I were going to check this in as baggage, I'd be worried about the rough handling the baggage jockeys would give it, but since I'll be doing the handling, it's just enough protection from dirty chain and loose parts.

Now I just have to shave that 1" off of the folded width.