So the issue I have had with hinges in the past is that you likely need to router out a section of the pvc for the flat part of the hinge to lay in, to allow functional articulation with the glass. I was working with melamine when I used to build cages, but this step always threw a wrench into the issue. Go look at one of your door hinges, and see how it sits flush with the wood and you will get what I am saying.
This right here is why I did sliding. Not to mention feeding the retics I can't get nailed as easy