Thanks for the advice everyone! Mz Pixel Queen, that's a crazy coincidence!
RavensGryf, I'm relieved to read you think Sky's looking normal. After looking at my original post again I'm noticing an inaccuracy. It's actually been closer to a year since I went to the vet with this problem. They've both lost their feathers and grew new ones multiple times since then, but her crusty cere has remained. It's not normal for a budgie's cere to remain in this state for that long, right?
I'll keep searching for another Avian vet. The one I visited has nothing but positive reviews on different sites so I'm a bit surprised.