I finally wised up and came up with a very simple and easy solution. I put all of the small bags into little cube storage containers. About 2-3 handbags can neatly fit into each plastic container. The container holds the bag upright and in place. Now, when I reach for a bag I just need to take out the right container and grab the bag I need without toppling the others over.
For my large summer handbags, I added a large extra coat hook onto the closet wall. This is perfect for storing over sized bags that are too big to fit on the closet shelf. And don't worry, once summer is over I'll have plenty of large fall/winter bags to keep there!