I'll try to make this as clear as I can
I just moved into an apartment built in the 50's...I think...and I want to install a ceiling fan in the bedroom. At present there is just a light fixture there. The apartment has been somewhat renovated, but the ceiling in the bedroom is still the original, and the electrical box in the ceiling appears to be an old one.
My first worry was whether or not it would hold the weight. I checked with the super, who told me that the guy living here before me had a fan for years. I had an electrician I know come by and take a look at it, and he said it should hold the weight with no trouble.
The problem is that before I had him look at it, I started to work on it myself and did a little bit of damage to the ceiling around the edges of the electrical box.
The reason for the damage is this: for some reason one corner of the box is flush with the ceiling, but the other corner is about an inch deep in the ceiling. Maybe at some point someone re-plastered the ceiling and did an uneven job...I don't know. But my first thought was that the bracket of the ceiling fan would have to be flush against the BOX, and so I started chipping away around the embedded corner, trying to make enough space for the bracket to tighten up against the box inside the ceiling.
Now I think this was a mistake. I should have gotten a longer screw to make up for the inch gap between the surface of the ceiling and the embedded corner of the box, and just tightened the bracket against the ceiling as it was. But now the damage has been done.
What I think I need is some kind of plate to place over the hole, wide enough to cover the damage. I would screw the plate into the box and then attach the bracket to the box THROUGH the plate. I found a number of plates at Home Depot that would be perfect except they have no hole in the middle for the wires to go through.
So here are my questions, if I haven't lost you already:
1. Am I right that I need to find some way to make up for the damage to the ceiling? Does the metal plate idea sound like I'm on the right track?
2. If so, do you know where I could get the kind of plate I need?
3. Or am I worrying myself over nothing, and there's really no need to give the bracket something to tighten up against? Could I just get a longer screw to make up for the embedded corner of the box and then maybe put a washer on the other side and be done with it? Will that make the whole operation less stable?
Here are pictures:

Looking straight up into the ceiling. The white part at the bottom is the damaged corner.

Close-up of damage. Difficult to see, but this corner of the box is about an inch inside the wall.

Here is the original bracket for the light fixture (NOT for the fan). I'm trying to show that one side can be screwed in flush against the ceiling, but the other side is kind of just hanging with the screw tightened only partially, to make up for the gap between the surface and the embedded corner of the box.

The gap between the surface and the embedded corner of the box is more visible here, as is the fact that the bracket is not actually tightened against anything.
Am I making any kind of sense?
Thanks.