We're 1/4 into Book 5, I highly recommend this campaign, it has a lot to offer and should please just about every playstyle.
From my experience it was best to drop the caravan, relationship stuff as it can be more easily resolved (I pretty well just fudged in some additional treasure to represent their share of the profits when the caravan reached a city).
The caravan works essentially as a mobile town for the party to come back to and engage with. I did have the NPCs on a revolving door to help with away missions for the first three books. I removed the elven ranger as she was too much of an adventurer role rather than a support role.
Re Ameiko, we had a somewhat regular player take her role which worked well. That player hasn't been able to make it for a bit now so it's less ideal. A GM does really need to underline that the party are all Amatatsu now (divine right etc.) so that Ameiko is not untouchable. I think your idea of removing her entirely by the end of book 1 works.
As far as needing to run Burnt Offerings I feel that is completely unnecessary but to each their own.