It seems like a predestined paradox to me, which is why I always just assumed that after the Time Crash Chronopolis was not founded again in the future timeline, despite FATE's logic that she must protect changes to the timeline so that Chronopolis could be founded. I have several reasons for this (all of which assume TTI is an accurate portrayal of time travel in the Chronoverse).
1) The boundary of the Sea of Eden would be protected by TTI. Chronopolis would not need to be founded again after the Time Crash for all of the events of Cross to be preserved.
2) Even if Chronopolis was physically moved into the past (discard boundary theory), FATE would not need to be concerned with the preservation of the timeline because Chronopolis would once again be protected by TTI.
3) FATE does a really shitty job of protecting the timeline from alteration anyways. Not only is contact repeatedly made between the mainland and El Nido (and vice-versa), but Chronopolis' mere presence there completely changes history and the area around which Chronopolis was originally built in the future.
So, I think it is reasonable to conclude that Chronopolis doesn't need to be founded in the future after the Time Crash occurs. I also think it is reasonable to conclude that FATE has nothing to fear about altering the timeline. So either FATE has a) an incomplete view of how time travel works (unlikely considering Belthesar's influence) or b) was specifically programmed by Belthesar to be concerned about the integrity of the timeline for some alternate purpose - perhaps related to his grand master plan? Perhaps Belthesar wanted to minimize major changes to the timeline so that he could limit the number of variables that he had to predict when orchestrating his plan? The more that El Nido was isolated from the rest of the world, the easier it would be for his plan to succeed, after all.
