The first thing I noticed on the first page you linked is that my AP's IP should be outside the DHCP range of the main router. So I limited that DHCP to 192.168.1.2 - 192.168.1.200 and gave my AP a static address of 192.168.1.201. So far everything seems to be working, although I'll keep a close eye on things through the rest of the day.
So far I'm optimistic. Thanks!

Well, that didn't go well. All my computers are now happily connected to the routers and the LAN, but they've all lost internet connectivity. All, that is, except my laptop (which I'm using now).
What I can see is that all the other devices have been issued new IPs (192.168.1.101 and up) - except for this one. The ISP router has a proper public IP and it looks perfect. But no other device has actual internet access. Any ideas?
I'm afraid the IP of this laptop could be renewed any time which will kill this access, too.

I assume the AP is hard wired to the main router?

As noted in the FAQ make sure the cable is plugged into a LAN port of the AP not WAN.

Make sure the AP's LAN address is configured correctly and is outside the DHCP range of the main router.

Make sure AP's DHCP server is disabled.

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It is.

Yup.

It certainly was (although I've restored the original setting to see if it would give me back my internet access).

Oh. Somehow DHCP was enabled on the AP. I have no clue how that happened...but it did happen.
Fixed now and everything looks good.
<Whew>

Glad that you found the issue. (It was mentioned in the guides as well).

I'm afraid I'm now back to where I started! There were a few weeks where all my NAT hosts could happily talk to each other, regardless of which AP they were connected to. But now some just aren't showing up. My Raspberry Pi, for instance, just doesn't appear in nmap results from my main workstation, but is getting its old DHCP IP from the primary router and can at least sometimes be seen from other hosts. And yesterday, I could only access one of my local hosts after having SSH'd in to it from a third host, and then SSH'd from there to my workstation!
So the routers are wired properly, the AP has a static IP (192.168.1.201) outside the DHCP range, and everyone has internet access. I can't think of anything I did to change the network configuration in the meantime, but I'd appreciate if anyone has any more ideas!
Thanks,

You have not changed any physical configurations or settings?

Are the missing hosts connected to AP or mixed wired and wireless?

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I've been trying to remember, but I can't think of anything. I know I hadn't even logged into either of the routers for weeks. I did just move the ethernet cable from one LAN port to another LAN port on the AP, but it didn't help. That, by the way, was in honor of my very first major networking problem many, many years ago when it turned out that one of the ports on a cheap hub I was using was flaky.

Right now I can't access a host that's connected to the same WiFi AP as my workstation:

There are several reasons you might see a no route to host message.

If you can ping the computer then you might not be connecting to the correct computer. Check the address in the router.
If the IP matches then ssh might not be running.
If ssh running are you using some port other then 22
If ssh is running then it could be a firewall setting which is probably not it.

Thanks. The IPs are correct and SSH is running at default settings on all machines. Everything is tested. No firewalls.

I think I tracked down the real problem causing me all this grief. I tried power cycling the TP-Link WiFi router and I got my full network back. I think something's falling over on the router over time that can be fixed with a reboot. I might contact TP-Link (it's still under warranty) to see what they have to say about this.
Sometimes it just comes down to bad hardware.
Thanks to everyone around here who offered help on this!