All these ready made Ubuntu derivatives have some unnecessary packages. Even though it is said not to upgrade from the earlier release to the newer, that’s what the devs do anyway, hence all kinds of unnecessary packages. For example, if the dev has a HP printer, he forgets to uninstall the drivers and so on from the final release. No one is going to start fro the very beginning to create the “next” release. In different derivatives, it is the filesystem.squashfs that (really) differs, The rest is same files with different distro names and different backgrounds for live booting. In the UEFI live boot, even the grub background is the same.
So, the idea to use the mini iso and add a minimal Unity to it. If the Ethernet is a problem, why not copy the Unity specific deb packages from one of your 18.04 Unity install. If you’ve not autoremoved and cleaned the system, some of them should be in /var/cache. Or, when the Ethernet is OK, just download all the Unity specific debs and dpkg them. That way, you’d create a clean Unity install.
The roundabout way, install Xubuntu 18.04 in minimal, then install Unity on it. Reboot and uninstall lightdm-gtk-greeter and reboot to Unity greeter. Then uninstall whatever unnecessary stuff left. You have to install Synaptic before uninstalling all that. You can see what is there and what is not needed in it.
You can use Lubuntu 18.04 instead of Xubuntu, but there you have to uninstall lubuntu-desktop and all lubuntu, LXDE stuff and Openbox, after installing Unity there. It is a lighter in size distro than Xubuntu. It is actually LXDE over Openbox so much lesser bloat there.
By the way, don’t touch Lubuntu 18.10 or anything newer, for they are bloated. You can see my trip to Plasma. Btw, I didn’t have ANY troubles in doing that, even though there is a suggestion at the end. The idea was to move it to Unity, and I’ll still do it.