I think you should slab the whole frame
...seriously though, a regular plastic protective sleeve works better. You can frame your pics just fine with those.
Maybe use a frame that is a little deeper and just use a thin piece of cardboard or regular brown paper to hold it into place. Glue it if you have to. For that matter, you don't even need a back. The pic is protected. Jam a thumbtack or a sharp object into the frame to hold the slab. You should be able to make it work.
Good Luck