^The answer to the "how so" is because it makes more sense for the ordering to go FS -> FSA with nothing in-between because of all the reasons already discussed in this thread, not the least of which is the fact that FSA specifically says that the people of Hyrule thought the land was at peace from the end of FS until the beginning of FSA. So whether that means FS has to be moved, FSA has to be moved, or they both have to be moved, the resulting FS -> FSA ordering would give us fewer contradictions than we have now.

Not sure if the Kakariko Village bit of info is the best evidence since TP confirms that there's more than one Kakariko Village in the Zelda universe (which means that FSA's Kakariko may not even be the same one that we see in the other games), and I'm not sure why you think we can glean the status of the kingdom during FS, considering that FS takes place in a secluded area far out of the way of the main kingdom. We don't know the state of the kingdom during FS, because the majority of the civilization is likely set up on the other side of Death Mountain rather than in the secluded area of Hyrule that FS takes place in.