maybe the same way that Roland can remember telling Eddie about the Boy when in fact, he did not, since the boy did not, in fact, die.
what I'm saying is, however that paradox is handled in the reality of the Tower, I'd assume that Roland having the horn despite the cycle starting from the desert would be handled in the same way.
I totally agree with the idea of picking up the horn indicating a completely different character as it is a valid assumption.
besides, as a gift from Gan...what's the point of putting Roland through all of this trial and error if its going to throw gifts at him that may or may not have major impacts on his quest after any specific cycle?
If we assume that each cycle is him getting progressively better at reaching the Tower with less pain and heartbreak in his wake, then what's the point of that?
I'm kind of thinking that explaining the Horn is probably difficult to do without explaining the nature of the loop.
also: in regards to the story we read being loop 19 and both 19 & 20 starting in the desert...all we really know is that loop 20 starts in the desert. If there was a prologue to The Gunslinger in which Roland stepped from the Tower's top to the desert, then it'd be clear that both loops started in the desert. But as The Gunslinger starts where we can only assume the loop has already begun (whether it started in the non-existent paragraphs before or long before that), we can't really know for sure that both loops begin in the same place.