Thanks @Andrew_Rowe for the tip!
No, I don’t need a connection from outside my LAN to test.
So I ran install-discourse with --skip-connection-test, and as expected, the installation continued without getting stuck on the domain check.
Just remember to stop nginx if it’s already running (outside of Docker).
But it’s working! Discourse is running in its container!
But… apparently we now have a certificate issue.
nginx: [emerg] cannot load certificate "/shared/ssl/forum.mondomaine.me.cer": PEM_read_bio_X509_AUX() failed (SSL: error:0480006C:PEM routines::no start line:Expecting: TRUSTED CERTIFICATE)
Of course, I followed this topic and verified the existence of /var/discourse/shared/ssl/forum.mondomaine.me.cer, and it’s there, along with the .key and two other files: .me_ecc.cer and .key.
I rebuilt the container, but the issue persists.
I can confirm that installing Discourse on a local test machine is a real battle! 
It’s clearly not encouraged.
And since there’s no simple solution (no, I will not use CloudFlare, no need to go down that road, thanks), I think this will be my last post on the subject. 