Is this for a book that's text or mostly images?

If the latter, they might need to look at Comic Book Creator (or something like that) that Amazon has for creating comic books.  I don't know if it has an option for a square eBook, but I would think it would allow for square panels which might be a possible compromise.

A few questions for you:
What's the actual End Of Life dated listed for Cloud Linux 7? Can you postpone trying any OS updates until sometime after your launch?
Why did you switch to an unsupported operating system? Can you switch back to a supported operating system rather than just doing this upgrade?
Have you considered fully-managed hosting? There are tons of providers, especially for WordPress, so you don't even need to worry about these OS upgrades or system updates. These are usually more expensive, but one call to a contractor may be more expensive than a year of managed hosting. (If you don't like Bluehost, perhaps you could ask for a pro-rated refund. Looks like they also have cloud, managed WP hosting which you could maybe ask to be migrated to, paying a difference in price as needed)

For the first question, June 30, so yes, I could postpone. But really, my launch isn't that dependent on my website. And there is something to be said for getting the earliest start possible if there could be complications.

Second, well that's a good question. Bluehost seems to sit on old OS software for as long as they possible can. Their documentation still refers to CENTOS 7 when the current version is 8.5. And CENTOS 7 also loses cpanel support on June 30, but there's no reference to that in any Bluehost document. There is an unofficial update for an inplace  upgrade, but it looks just as fraught as the CL update. So even if I downgraded from CL to CENTOS (which might be marginally less fraught), I'd still be a little less than three months before end of life with no clear path forward. But at least that situation would be recognizable to Bluehost.

As I recall, I did the switch from CENTOS to CL thinking that I was getting CL 8, which would have gotten me out of the update box for a much longer time. The change from CENTOS 7 to CL 7 wasn't fraught at all, but it didn't get me where I wanted to be.

Also, the commonplace suggestion at the time (and still, for that matter) is to migrate to another server (!?). If you're a business with a large IT department, great. But someone like me is dependent on the hosting provider--unless I want to switch providers. I have no problem with Bluehost normal operations, but their support is a little...less than one might want. Switching from a lesser plan to VPS resulted in a downgrade of my PHP version (all the way down to one that was barely supported anymore). Easy fix, but still not something that should have happened. And support wouldn't have figured it out if I hadn't pointed it out to them.

I'm pretty sure there is no prorated refund, but maybe I actually would be better off shifting providers. That is a hassle in itself, but some of the better ones offer a free migration that might well be worth it.

Anyway, I have to go now, but thanks for the advice.

I am in need of hive-mind advice on a particular issue. It may not affect anyone else, and it's possible no one else has experience with it, but I thought it was worth a shot.

I have self-hosted Wordpress using Bluehost.

My issue is on the backend. It's a cpanel site that was running on CENTOS 6. BH updated to CENTOS 7 some time back, but CENTOS 7 has been nearing end of life for a long time.

A while ago, I managed to switch from Centos to Cloud Linux 7 (BlueHost doesn't forbid the use of Cloud Linux, but it doesn't offer any update support, either.) Cloud Linux 7 is about to lose cpanel support.

Unlike updating an OS on your computer, which can be relatively easy, updating a server OS can be a real headache. Cloud Linux has designed an update pathway from CL 7 to CL 8. Hurray, that should be easy. But CL also recommends the operation only be attempted by an admin with advanced skills. That isn't me. And the introduction says basically, "This could work, but it could also blow up in your face and make your site inaccessible."

Of course, I have backups. But unlike backups of the computer, if the site is inaccessible, I have no way to restore from a backup. Hypothetically, Bluehost could, but my support experience hasn't been great with them. For a much simpler thing than this, I wasted hours before finally getting a solution from the third person I dealt with.

Logically, I should hire someone to do the job. But hiring someone for a CL serverside update doesn't seem to be a thing.

(As I type this, I realize it's ludicrous to expect anyone to have an answer to such a specific problem, but I've come so far that I might as well finish.)

Here's the only plan I can think of:

First, redirect my fans at the beginning of next month. Host a planned giveaway through the giveaway provider's own site. Link to Amazon rather than my own site for my new release. In other words, set things up so that my site could be down for days without creating an insurmountable problem.

Second, backup, recheck all the instructions, run the preupdate check. Fix what the preupdate check tells me to do (long, fiddly process, but probably doable)

Third, attempt the update. If it works, hurray! If it doesn't, then,

Fourth, work with Bluehost as long as it takes to get the thing back up. CL support and/or cpanel support may also have helpful hints.

Writing this is therapeutic in that I feel as if the worst case scenario is losing a lot of time. I can endure that.

An alternative course would be to switch hosts, in which case, I'd start with newer server software and not have to deal with the update issues. Downside is I have a three-year plan with BH, most of which still remains, so I'd lose a lot of money. I could do that if all else failed. (I'd also have a frontside backup, so I could migrate that part to another server.)

Anyone have any suggestions to improve upon that strategy?

Thanks for reading. 

That was my thinking as well. I just wanted to make sure I wasn't missing something obvious.

I'm not sure what the motivation is, but the author really wants the ebook to display as a square. I found software called Book Creator that will produce such a thing if desired, but it's for school use and doesn't seem especially well adapted for regular book production.

That doesn't make much sense.

A square cover is of course possible, since Audio covers are like that.

But square eBook inside? That really doesn't make much sense.

It would be relatively easy to do though. You just set up a custom square paper size inside Word, and set it the top of the document. It should then put a soft page feed when the square is used. Might be a bit more complicated than that, but should be possible. You'd have to use the right view though. And maybe put a hard page feed in before uploading.