What is the absolute simplest way to accomplish this?

< gets on soap box>

The absolute simplest way is to use IPv6: on your Debian machine, assign multiple IPv6 addresses, one for each service you want to expose to your LAN. There’s no penalty with having a dozen v6 addresses.

Although you have those addresses, your machine generally uses just a single one for its own outbound and inbound traffic. For each service, you would edit their config so that they bind to a specific IPv6 address. Finally, you would configure an AAAA entry in DNS so that your chosen subdomain will point to the IPv6 address in question.

As an example, suppose you had three different web servers running Nginx, currently on port 80, 8081, and 42069. What you would change is the server config for each server instance, adidng the IPv6 address as part of the “listen” directive. Since each instance is now bound to a different IP address, nginx can now listen to the conventional port 80 and n’ary will the three collide. In other software, the configuration option you’re looking for is the “bind address”.

For a home network, you might have a single /64 IPv6 subnet. But that still means you literally have billions upon billions of addresses to use before you ever run out. And as you’ve recognized, using DNS names to identify services is a lot easier and intuitive than using port numbers. It also neatly avoids the need to memorize IPv6 addresses, because that’s never been necessary: we have DNS.

< gets off soap box>