The empty isolinux.cfg is a know characteristic. If you use refracta2usb to make a multiboot live-usb that uefi capable, it will actually put an empty isolinux.cfg on the usb so grub can find it. All the other isolinux files get renamed as syslinux in that case.

While doing so I found some bugs in the desktop-live ISO image.

In boot/grub/x86_64-efi/grub.cfg there are both incorrect entries (insmod with *.mod) and non-existent entries (insmod ieee1275_fb, insmod vbe, insmod vga), which generate error messages during boot. Actually, all insmod entries are unnecessary and should be removed (i.e. only source /boot/grub/grub.cfg should remain) once the error in boot/grub/grub.cfg is fixed.

In boot/grub/grub.cfg the first line must read if loadfont /boot/grub/font.pf2 ; then in order for the following statements to be executed!

By the way, the directory efi seems to be unnecessary, because its content is already in boot/grub/efiboot.img. Furthermore, grub/x86_64-efi/{config.h,kernel.img} seem to be unnecessary.

For a UEFI boot only USB stick, a virtually empty directory isolinux is sufficient, containing only an empty isolinux.cfg.

I did all this for my ISO image and after xorriso-ing an edited boot, an "empty" isolinux and a copied live the USB stick boots perfectly.