I would like to have a full installation of Slackware on a flash drive, just like I have others - Debian, Mint, Fedora, Arch

Here's the skit.
I used a Slackware live usb stick (/dev/sdc) to install Slackware to a different usb flash drive (/dev/sdb). Didn't have a problem with the console based process.

First I used the suggested partitioning scheme, without a small EFI bootable partition. At the bootloader step I was offered the option to install to my hard drive (/dev/sda1) Not what I wanted.

Then I started over and made an EFI partition as /dev/sdb1. Same option given. I thought I would try the install to usb stick option. "No new usb stick found, but if you had inserted one, remove it now."

Then I was offered to install Elilo to the hard drive. Not desired.

Any suggestions will be attempted until something works. At that point I will likely stop.

Either with Ventoy or not, you can go with the first flavor https://docs.slackware.com/slackware:liveslak

Be sure to read the page to the end.

1 members found this post helpful.

This is a general how-to to manually install the bootloader. Skip the lilo/elilo prompts, chroot into the system by opening a shell at the end of the installation, format the usb efi partition fat32, edit /etc/fstab for the correct efi partition, unmount /boot/efi and mount the usb efi partition to /boot/efi, run grub-install, grub-mkconfig to install grub bootloader and create a grub menu, or run eliloconfig if you prefer elilo, exit the chroot and reboot.