I bought a used copy of Across the Pacific some years ago. Haven't read it yet. I'll try to tackle it this year. I do have both Shattered Sword and Zimm's book - was looking through Shattered Sword this evening, and hunting for Zimm's book.
To GB, I am enjoying this story.
Across the Pacific is dense reading in some ways, but worthwhile - kind of like reading Sansom's books on history of Japan.
I don't claim to be well read in naval history, but of what I've read, Shattered Sword is not only very readable, but really landmark, and the best naval history book I've ever read. It also benefits also from the author's computer graphics professional connection - very good diagrams and maps - a shortcoming in a lot of books. I found the technical detail about the nature and operation Japanese aircraft carrier's in general very interesting - like the fact that the Japanese carrier island was like a naval version of the 1 or 2 man tank turret. The last several chapters on the outcome and big picture stuff are as important as the content on the battle itself - and very relevant to even this timeline - good general discussion of Japanese strategy and some further references. One comment I forgot to add in my initial post that I think is vital is his simple and clear discussion of doctrine and practice, even exceeding Zimm the professional here maybe: its a tether, military's don't just do things in vacuum or change practice in an instant, things are done a certain way because that's how they trained - in general. Simple point, but a pretty important one. Many times on this site I think that's a point lost.
Another author I mean to get into reading for the purpose of understanding the Japanese mindset is John Dower and War without Mercy, though I don't hold with some of his pacifist views - have his Embracing Defeat as well.
Zimm's book was easy to find on Amazon and affordable:
https://www.amazon.com/gp/product/1612001971/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1
I got through reading it partly, by jumping around some, and not reading it straight through. Can be a slog in places. Read the Amazon reviews in depth, starting that recently, but wishing I'd done it a long time ago - so obvious - sometimes the negative or critical ones are the most helpful to sort out whether the rest of the reviews are a lemming stampede, or just to form a more measured, complex view and get more info beyond the book. On the PH book, there's some really interesting back and forth between a descendant of Kimmel - trying to defend him as being a scapegoat - Zimm is pretty harsh and clear about Kimmel and uses a Naval officer's perspective to be so.