We've seen lots of articles about the technical details of setting up a mail server (software to use, how to configure it, etc.)

Can you suggest any article that talk about "checking common greylists" and other steps admins should take when their email is failing?

One of my tenets is that it's fairly easy to learn to do anything, but expertise comes from knowing how to fix things when they go wrong, which is harder to come by.

I can see how to setup the email server, but the stuff you're talking about is just dead goat voodoo.

If you buy your own ip range you will be fine.

I used to work at a company who owned 128 address and the mail server was one one of them. A Whois lookup of the mail server IP gave my old boss as a contact person. Not just some random ISP.

We did not setup DKIM until maybe 2014 and that was not really necessary from a outgoing mail perspective cause we never got emails bounced.

I don't need many IPs, any tips on what it takes to own a /29 and how to go about buying it?

I don't believe PI space comes in anything smaller than /24.

Then, given what I've read about how tight IPv4 supply is these days, I conclude I probably can't afford it. :-)

There are places to buy smaller ranges. Free Range Cloud lets you buy a static IP tunnel or lets you buy a /29 through them. The problem with smaller ranges is that you can't actually advertise them through BGP the way you would with a /24. https://hoppy.network/ also gives you a unique /32 v4 and /128 v6 if you'd like.

I believe you will like this then:

How to acquire 1,024 public IPv4 addresses which are worth $60K for $500 - https://news.ycombinator.com/item?id=29844651

That requires colo, I think? So more work for self-hosting and maybe expensive.