Welcome Dale.
I'm with you that I've never liked the idea of throw over bags for the same reason that you listed. If you are going to just keep the bags with their brackets then I would stiffen the bags up for the mounting process. What I did was cut two pieces of plexiglass for each bag. I inserted one into the bag and the other to the outside, sandwiching the motorcycle side of the bag between them. This should give you the versatility and stiffness for you to mount them any way you like. Once on the bike you can't see the exposed plexiglass at all.
