I repacked the stuffing box in the water. It's dripping multiple times a second at the moment because I read I am supposed to wait a while before tightening it down so that it can get water logged. I plan to motor around 4 hours tomorrow and then give it some adjustments.
As suspected, my shaft is scorched and scored. So, I'll have to replace that when I next haul it out of the water.
I'll just pretend that this problem already existed when I bought the boat -- which could be true. But there is a reason I bought a cheap (but quality) starter boat to make mistakes with.
Here is a photo of the old stuffing and the shaft. I can feel where the shaft is worn down in spots:
https://photos.app.goo.gl/SkTduWSA4wTCHduBA
What are the side effects of the shaft being warn down? How do I know when it has reached an unsafe amount of wear? I am hoping to do another 650NMi of motoring before my next haul out.