This is probably a good time for a reminder that the only authoritative explanation (so far as I recall at the moment - are there others?) of the natural/necessary classification (aside from the scholium in DL which is of uncertain source) is that of Torquatus in On Ends (Reid translation).
Cassius I'm not sure that I'm reading your post #30 correctly but, for reference, here are PDs relevant to the categories of desires:
PD26 The desires that do not bring pain when they go unfulfilled are not necessary; indeed they are easy to reject if they are hard to achieve or if they seem to produce harm.
PD21 One who perceives the limits of life knows how easy it is to expel the pain produced by a lack of something and to make one's entire life complete; so that there is no need for the things that are achieved through struggle.
PD29 Among desires, some are natural and necessary, some are natural and unnecessary, and some are unnatural and unnecessary (arising instead from groundless opinion).
PD30 Among natural desires, those that do not bring pain when unfulfilled and that require intense exertion arise from groundless opinion; and such desires fail to be stamped out not by nature but because of the groundless opinions of humankind.