Currently, during Slackware64-current installation on a machine with an EFI firmware, the script eliloconfig allows to install a simple (read: without a menu) elilo boot loader, and to register a boot entry for Slackware in the firmware's own boot menu.
The elilo documentation in /usr/doc/elilo-<version> taught me that it is also possible to provide a text menu displaying the available boot entries known to elilo, and help texts displayed when pressing function keys, as allowed by syslinux. I tried, and it works!
So I have modified elilo.SlackBuild and eliloconfig and added help text files to the source elilo directory to build such a menu.
This stuff is available @
https://github.com/DidierSpaier/eliloconfig
As this version is primarily intended for Slint and other Slackware derivatives like Salix, eliloconfig is internationalized and the SlackBuild by default installs corresponding translations.
However it can be used to build and install an alternate elilo package for Slackware as explained in the README, without translations if that is preferred.
The menu and help screens are shown in attached pics.
The menu is displayed at boot time whether or not an entry for Slackware has been added to the firmware's boot menu. If not but the firmware is equipped with en EFI shell a provided startup.nsh script starts elilo that displays the menu.
Also, additional boot entries can easily be added to the menu just editing the config file (as you would do with lilo, but without the need to run a command afterwards), including for other systems, provided that their kernel and possibly initrd lie in the same EFI partition.
This has been tested in virtual machines and on bare metal (thanks to laprjns), but more testing never hurts, so thanks in advance for your feedback.
PS Only caveat: the build fails if done on Slackware64-current (as does the genuine Slackware elilo build as reported here). However the package built on Slackware64-14.1 can be used on Slackware64-current.