I would think there are some Furniture or Objects Conservators near you that could take this on. I have frequently tackled similar problems, and usually there is a way to work through this problem. Ideally, some more information would be optimal.
I'm assuming since you say it is an 'antique' that it is a skeleton key we are talking about. If so, that helps, as these are much simpler locks than more modern locks. Also you did not specify if the lock is 'locked' or if the broken key is just 'jammed'. I'm assuming it is both locked and jammed. If it is only jammed but not locked, removing the mortise should allow you to clear the lock of the broken key.
By 'China closet' I am assuming you mean a piece of furniture (also known as a 'cabinet', 'hutch', 'sideboard', and etc.), though I suppose it could also be a single door the a more traditional 'closet' containing China. I'm also not sure if you are talking about a door panel or a drawer, and to some extent it might not matter.
Regardless, you might be able to pull the hinge pins and get through a door or panel that way. If it's a drawer, you might be able to open a drawer above it to gain access to the locked drawer from inside and behind. Typically antique furniture uses a 'mortise lock' which fits into the drawer front, either with a true mortise (a pocket cut into the top of the front panel of the drawer), or they are attached to a similar cutout on the backside of the front drawer panel. If it is the former (a true mortise), that makes removing the lock from behind more difficult, but if it is the latter, and you can get access to the back of the lock, often the screws can be (admittedly awkwardly) removed, and the drawer unlocked by removing the lock.
I hope this is helpful, take care, Tom
------------------------------
Thomas Braun
Objects Conservator
Minneapolis MN
(612) 824-6121
------------------------------