I have a 16.04 install with / and /home on separate partitions; I would like to install Ubuntu server 18.04 on the / partition without wiping out the /home partition; this is possible with a xubuntu desktop iso installer, but apparently not with the Ubuntu live server 18.04 iso; it just deletes all partitions as if the disk is empty; on the positive side, it correctly partitions a new disk and installs the efi partition correctly and it is actually bootable; no need to run sudo grub-install after the install from a live USB to make the new install boot.
First of all I would make a backup of your home directory and save the /etc and /var/log directory.
In the Ubuntu 18.04 installer you have to choose in the partition menu something else.
the ubuntu server image name that allows you to choose which existing partition(s) to use and how, similar to the xubuntu desktop installer, is