The thing I hate about my medicine cabinet and what you would have to watch out for (If you were still going to do this project but, I see that you are not) is that the back wall of my TT is inclined to the front of the TT and that is where my cabinet is mounted. They put the bottom of the medicine cabinet on a 2X1 to make up for the lean but, it is not enough and the cabinet leans forward. So, I can put stuff in it but, the slightest little bounce makes it fall over and when I open the door stuff falls out.
The good news is that I am learning to be a better catch this way.