I killed cats on the island while I was indifferent to avoid having to clear the way. I would do the rat teeth quest(I also eventually did others, almost all of them except for the Eruditehide Tunic and Rough Shoulderpads) mentioned earlier in the thread to restore my faction. It did raise my faction.
As for the problem with two different factions. Back in the 2000 of December there is no record of "Kerra", I went three years ahead (2003) and still, no sign of it. The earliest sign of it was 2005.
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No kerra faction.
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The same faction but now called Kerra faction (no longer called Kerra Isle)
Either way, the quests in the zone did raise the factions with the same cats in the zone. Some were KoS to all (some tigers, fangtooth). It could have been called faction UberCats and still raise the faction they were on. Regardless of the name, whatever faction they are on, the quest boosts that faction.