I haven't been able to get the picture yet, but I am convinced now that it is combination of both rot and some sort of bug/pest. I inspected the plant yesterday and I found a very small whitish/grayish bug that had antenna and little markings on it's body across it like that of a rolly polly but much much smaller. So I treated it with malathion and removed the two leaves that looked infected with rot. I will do the Physan early tomorrow morning because I won't get home till dark tonight.

I rent so I don't have any clue what the sprinkler system is, but I would guess city water. That is the same as what I water with most of the time unless I have rain water. I moved the plant so it shouldn't be getting hit with any more water at night.

I will definitely not remove any basal sprouts if they do happen to grow for me.

Thank you for all of your help so far! Hopefully this plant can be salvaged.