I am a Home Depot associate, trained and authorized to help people on the internet. I think it is very possible to convert the doors from sliding to hinged. It looks like you can just remove the bottom tracks and add in a solid piece of wood so that it would fill the entire track area. this would give you a stop for the doors on the top and bottom. Then as budro said there are many different types of hinges out there. if you want to go with the style that you have to drill the holes in the back of the doors I would suggest that you invest in the jig that gives you the correct placement every time. If not there are many other surface mount hinges that go well beyond the 90 deg. Here is a pictures of the one that I have used a few times.. The one picture shows you all of the ways that you can hang the doors with these hinges. I hope this helps you out. Please post some follow up pictures. I would love to see how it turns out.