Ideas for addtional support for bathroom cabinet contents

Silverware drawer inserts may help. That is what I use. The other thing that may help is anti-slip sanding mat, like what you can get from Rockler. If you are handy and like building cool custom stuff, you can buy plexiglass sheeting. Heat it with a hair drier, or paint stripper gun, and bend the plexiglass edge so you have a flange to keep things in place.