I've tried the cleaning and repacking method ona few headsets. One was a king, the other I can't remember but something high end, American classic, white industries or something like that.
In both cases it didn't really help. If the races in your bearings are fine, I don't see why it won't help, but if the races are pitted or the bearings damaged then it's not going to help much.
I have in the past had to remove bearings that were pressed in but goosed and I can see more room under the ones in the race Face pictured to get a bearing puller, or cruder method to get the bearings out.
If you can then find the size, buy some decent quality new ones and press them in.