Hehehe.... I think I finally got this one figured out!
Okay, bear with me for a second here. I've had this theory laying around for a while now, never having posted it because of my own personal issues (lack of self confidence) and not wanting to create a new topic for it.
I developed the theory trying to use only as much proof of actual in-game evidence to explain this paradox, as opposed to the rest of them based mostly on other assumptions (like using the entity to explain everything); therefore making some of them seem as something that is not really convincing enough, since they don't make proper use of much evidence, to fully explain or give us a reason as to why they are to be believed in the first place.
First of all, consider the following part of the script concerning the Moonlight Parade ending:
Marle: You're my distant ancestor.
So you'd better have tough kids or I'll be in trouble!
Kino: Heh, Heh!
No worry. Ayla VERY strong!
Marle: Right!
(puzzled by this, she pauses for a few seconds, blinking repeatedly)
Marle: Hey... what do you mean by that?
Now for my theory, consider that Ayla is not really Marle's ancestor. In other words, she could NOT be the one who actually gave birth to the descendants who would eventually become the Guardia royal family. She simply cannot be her relative, as the paradox would come into effect, and we know that never happened, besides this is NEVER really stated in the game. So the general assumption should be, from now on, that only Kino is, which is mainly because of two reasons: 1. Kino is the one introduced as to be her kinsmen. 2. The above scenario that was quoted from the game, DOES make one raise the question that Marle asked Kino, and never got an answer for.
I guess the only reason people assumed that Ayla was to be considered also as her kinsmen is because she gets married to Kino in the playstation ending. But, other than that, the game never makes this evident in any way. Now, for some reason people don't find it strange that they don't get along very well and are very untrustworhty of each other. Ayla yells at Kino for having taken Crono's stuff (the Gate Key) because he acted out of jealousy thinking that she probably liked kim best. This clearly demonstrates the nature of their relationship. They don't trust each other.
For example, like I said, in the Moonlight Parade ending, Ayla yells at Kino (yet again) for having said the above statement to Marle when she mentioned that she would be in trouble if they didn't have strong children. It seems, that Kino's comment was more focused towards the word 'trouble' than 'kids' and answers her that way, as if to say something about their own problems. Ayla then calls him a 'dummie' and immediately prones to take off to their time (as if to shut him up), before he says something 'stupid' (anything else) to Marle that's none of her businesss. Like for instance something about their personal relationship and what it exactly involves?
So if you take into consideration all of this information, you can get a very plausible answer to this paradox. And the answer (if you follow the Ockam's Razor Principle) is this: Kino, being the real ancestor to the Guardia Royal Line, was able to time travel to 1000 A.D. to the Moonlight Parade Ending, because he had already fathered a child in his time period (who knows, perhaps during the time that Ayla was gone for the adventure with the team), and therefore not creating any Time Paradox in doing so.
P. S. I realize that there already is a theory called Alternative Ancestors by KerntheGerm & Daggart that tries to explain this, but doesn't really go into any in-game evidence or details that could demonstrate this further.
