So I’ve got a couple of services that I access using mydomain.org:1234 for example, but since Nextcloud runs its own web server it’s hosted on mydomain.org/nextcloud.
How do I set up my services so I can access them from a friendly URI like Nextcloud instead of ports?
Reverse proxy maybe?
mydomain.org/nextcloud gets reverse-proxied to mydomain.org:1234 and will appear as the former.
Yep this is the way. What OP wants can’t be done with DNS.