What do I have? Replacement closet hardware

Unfortunately, I was not able to locate matching hardware for the parts you show in your photos. They may be a little too old for us to get a hold of. 

Before I say anything for sure, can you confirm the diameter of the nylon caps on the end of the pins? Can you also tell me the thickness of the doors? Finally, please verify their material. I assume they are metal doors but I'm not 100% sure.

As for how to uninstall this hardware, removing the brackets seems to be the correct way in your situation. Old fashioned parts like this aren't always simple to take off, unfortunately. 

If you are handy and willing to experiment then there may be an option for you. Being that your doors are wood, you could drill 3/8" holes about 1" deep and 1" in from the end into the doors at the top and bottom. You would then tap in three 23-122 spring loaded pins for the top pivot and the top and bottom floating guides. 

For the bottom corner pivot, you would use the 23-231 with a 21-100 cap on its end to fit into your pivot bracket. The pin is threaded, so you can adjust the door to square up in the opening. It might make your life easier going forward, but it will take some work in the short term.

Yes, that is generally the kind of configuration you want on this kind of door. That will allow it to operate smoothly and still pivot when you need it.

You're welcome! Please let us know if we can be of further assistance.