Hello Tom, although I don't know what the set up on your oven door looks like, you could try dismantling it or part of it.
If you open the door and look at the inside face, are there any screws which hold the two halves together either on the inside face or possibly the edge of the door?
Try removing these screws (if there are any) to see if the two halves can be seperated. If this is possible you may well gain access to the broken part of the hinge.
Alternatively, are there any screws or bolts around the hinge area which could be removed to reveal more of the hinge itself?
As you dismantle the door it might be worth taking a photo or two to make re-assembling easier.
G.S., August 2008