"Precocious" Lactation and Salty, Foul Goat Milk

We only had one goat kid this year. But our other goat, Honeypot, started spontaneously lactating about the time Licorice had her kids. Honeypot had been dried off last winter, in hopes that she would get pregnant by the buck that was here for breeding. But even though she didn't get pregnant, she's lactating, so we are milking her. She doesn't produce more than a pint a day, and for the past week, we have only been milking her once daily. We're hoping that her milk improves over time, and with more milking. But I tasted her milk this morning, and am still finding it tastes salty, slightly foul, and super thick. And her udders don't show signs (swelling, abnormal heat, etc.) of mastitis.

I've done a little research about spontaneous lactation, and read somewhere online that it can be caused by pretty much anything that influences the doe's endocrine system: the presence of a buck, a false pregnancy, or, perhaps in this case, maybe, the pregnancy of a sister-doe?

Whatever the case, looks like from this thread that if a doe is lactating, and she doesn't have mastitis, it's safe to milk her. I'm also reading here that "it must be stressed that drying off the spontaneously lactating doe is not an easy task, and requires a management and treatment plan if to be successful." Lastly, this post on a homesteading forum said that it could be that we should milk three times a day and the taste issue may clear up. That said, though, the aforementioned post is referring to a goat that had not yet lactated before.