You can see here:
The dead bolt is too low and a bit too forward for the receiving hole. The bottom bolt's hole is too low as well, but it still makes it.
Here are the holes:
And the bolts:
Although the bottom hinge appears to be a bit loose, it doesn't seem to be the cause of this problem. That would be the fault of the upper hinge, but it seems to be working well. The alignment of the door to the frame is good, and is not mis-aligned.
Most advice on the internet says to just Dremel grind the hole lower and larger, but I'm hesitating because it's not just a strike plate, but a whole door frame than I would be modifying.
Is grinding or filing the hole larger the only way?