Triple Boot Mac/Win10/Ubuntu: how to restore original copy of Windows EFI to ensure boot to Windows still works

Possible Reason Windows Will Not Boot

The Ubuntu 18.04.3 LTS 64 bit installation software changes the Master Boot Record (MBR) partition table on the installation drive to cause hybrid partitioning. This would prevent Windows from booting on 2016 model year Macs. In 2012, Apple started to phase out the need for hybrid partitioning. Evidently, the Ubuntu installer does not check for this. The answer you reference has been changed to add a step where gdisk is used to remove any hybrid partitioning imposed by the Ubuntu installer on the installation drive.

You can also remove the hybrid partitioning by booting to the live version of Ubuntu from the installer flash drive. The steps are given below.

1. Download the latest Ubuntu installation ISO file from the Ubuntu Home Page. The file download and used in this answer was named ubuntu-18.04.3-desktop-amd64.iso.

2. Use Etcher to create a bootable Ubuntu flash drive installer, then boot from this flash drive. A tutorial can be found at the Ubuntu website Create a bootable USB stick on macOS.

3. When the menu below appears, select Try Ubuntu without installing.

   

4. When the Ubuntu desktop appears, press the control+option+T key combination to open a terminal window.

5. Make sure the drive is not using hybrid partitioning. This can be accomplished by entering the command given below.

   sudo gdisk /dev/nvme0n1p
   

   This command is interactive. The interactive commands you will need to enter when prompted by gdisk are given below.

   x
   n
   w
   y
   

6. Finally, enter the command exit to close the terminal window.

Possible Reason Ubuntu Will Not Boot

Below is a copy of an image you posted as part of your question with respect to steps 15 and 16.

The image shows the following message.

Warning: Filesystem is FAT32 according to fat_length and fat32_length fields,
  but has only 51068 clusters, less than the required minimum of 65525.
  This may lead to problems on some systems.

This warning occurred because the drive on your Mac has a sector size of 4096 bytes. However, the answer referenced an example Mac with a sector size of only 512 bytes. In other words, the new EFI partition you created was too small. The instructions have been changed so the new EFI partition is at least as large as the original EFI partition. In your case, this should be about 315 MB.

To create a larger new EFI partition, you will have to reinstall Ubuntu.