Old Decrepit Doan (as I call Doan form the ruined future) cannot possibly exist in the saved future. If a Doan exists in the new timeline at all, it would be a different person - Distinguished Healthy Doan, if you will.
Old Decrepit Doan is just that - old and decrepit - because of the world in which he lived: A world barren of simple resources (like food) as a direct consequence of the Day of Lavos. Once Lavos was killed, if time changes are indeed 'instant', then that Doan and the world in which he lived ceased to be, replaced by a future that contains many wonders. Like FATE, for example.
Now, since a countless number of people survived beyond 1999AD due to the actions of Crono and Co, that would in turn mean there would be countless decedents of those people, all the way up to 2400AD. On the flip side, that means that the people who had survived in the ruined timeline would now, in the saved timeline, have more options when it comes to potential mates to have children of their own. Thus, there is no guarantee that the chain of ancestor-decadents that would eventualy equal Doan would ever occur.
But lets say that all the right people needed got it on all the way to Doan's birthday. This new Doan, Distinguished Healthy Doan, would have no knowledge of the ruined future, no memory of Chrono's party bringing him seeds, and no idea why the future would need saving.
Ergo, Moonlight Parade Doan could not be Distinguished Healthy Doan from the good future. He can ONLY be Old Decrepit Doan. And therein lies the problem.