The design is pretty simple and mimics what a parking rack would do. But bikes need to be secured in 2 places - the wheels and the top tube. The bikes not only need to be secure, but in such a way that they stay away from each other. There is a reason good bike racks exist and they are specific to the task. You have a few things competing against you as well. 4 bikes on a single rack is a lot to ask and all the way back at the back of the RV they are subjected to a lot more bouncing around.
You may want to look at something more like this:
tray rack