Your logic makes sense, but I don't think that's necessarily how those phrases are used. Truthfully they are interchangeable. In your first and last two examples I would probably say B, the start doing variation, just to save on words, but both feel equally natural. Started souring sounds a little odd to me, just for the word sour, but it works fine.
Your third example has nuance. Both phrases work, but there are multiple implied meanings: "I haven't done my work and I will start doing it now." Or "I haven't done my work and I will start to do it from now on."
One is more towards the future and the other is more towards the present. You can still use them interchangeably though, and the difference will be clarified in context, i.e. "I will start to do my work now" or "I will start doing my work later." Basically, if you're speaking in present tense and you feel there's any ambiguity in the situation, just clarify when the action starts with "now" "later" or some context like that. Otherwise both variations feel natural.
