The T-Bag Dekker Supreme that I bought fits perfectly now. I removed the bottom and rear inside pads and now the bag conforms perfectly to the rack and sits flush on the base of the rack. With 3 sides and the lid still padded, the bag completely maintains its' shape, so there is no problem there. The more of those pads you remove, the more storage space you have also.
Another thing that I did was shorten the straps a little. The straps that come on it are way too long for mounting on a luggage rack. I cut off just enough that there was enough left to secure it and have enough remaining strap to fold about a 4 to 5" section once, and then a second time, so that you have the end being three strap layers thick, which fits fairly tight into the "belt loop" that keeps the extra strap from flapping. Then, take that 4 to 5" section that is 3 layers of strap and tie it in the middle with a plastic tie. That will keep it together so you don't have to redo this everytime you put the bag back on, and the plastic tie adds just enough thickness that you have to force the tie into the "belt loop" and that makes it real tight, and you won't have to worry about the straps coming out and flapping around.
Photos below to explain what I'm talking about. First, this photo shows how the bag fits flush now.