pebcak
10
What I still fail to see is how you can get to the submenus without getting the menu first. 
Anyways, we could try rebuilding the whole Grub environment from scratch and see if it will work:
The step 6 may not be necessary. If you still want to perform it, adapt it to match your system:
--efi-directory= ##the mountpoint for your ESP
--bootloader-id= ## the directory where the bootloader binary is installed