How do I fix a Grub problem associated with a clean install?

Question

I have a home-built machine with an Asus Sabertooth X79 mother board. It has an EFI firmware that I use to select boot disks, and contains multiple disks: 1 for the Linux install, 1 for the Windows, and 1 for backup.

I had Linux Mint 17 installed previously, and wanted to upgrade to 18. I figured that a clean install would be a good idea, since I can do that at this time. I partitioned the disk, placing one swap and one Ext4 partition, and installed using the Linux Mint version 18.1 MATE 64 bit live disk. On reboot I get the error:

error: no such device: 00000000-0000-0000-0000-000000000000.
Entering rescue mode...
grub rescue>

Searching lead me to try this solution. Implementing it confirms that the correct partition is identified as Boot. Running the last command gets:

mint@mint ~ $ sudo grub-install --root-directory=/home/mint/temp /dev/sda
grub-probe: error: failed to get canonical path of `/cow'.
Installing for i386-pc platform.
Installation finished. No error reported.

On reboot, I get the same error.

Implementing this solution on a fresh format/install leads to an error before reboot. On the last command I get the error:

root@mint / # sudo grub-mkconfig -o /boot/grub/grub.cfg
sudo: unable to resolve host mint: Connection refused
Generating grub configuration file ...
Warning: Setting GRUB_TIMEOUT to a non-zero value when GRUB_HIDDEN_TIMEOUT is set is no longer supported.
Found linux image: /boot/vmlinuz-4.4.0-53-generic
Found initrd image: /boot/initrd.img-4.4.0-53-generic
Found memtest86+ image: /boot/memtest86+.elf
Found memtest86+ image: /boot/memtest86+.bin
  /run/lvm/lvmetad.socket: connect failed: No such file or directory
  WARNING: Failed to connect to lvmetad. Falling back to internal scanning.
done

On reboot I get the same error.

Any hints about what's going wrong here?

Based on the chat with @Bahamut, I found this this information on dual booting UEFI. Based on that, I was able to see that I needed to select the UEFI boot option from the LiveDVD. Attempting to install that leads to the error:

The 'grub-efi-amd64-signed' package failed to install into /target.
Without the GRUB boot loader, the installed system will not boot.

On closing that window, I get an "Installer crashed" window that promises to allow me to file a bug report after closing the window, but no such bug reporting is done. In fact, the window doesn't close when I click "Close".

Final Edit: I was able to successfully install Linux Mint MATE 64-bit 17.3 (Rosa) using a live DVD, and then upgrade in place to Linux Mint MATE 64-bit 18 (Sarah), and then again to 18.1 (Serena). It looks like there is either: an error in the iso I downloaded, or a bug in the 18.1 64 bit MATE live installer.