Windows Backup error 0x807800C5 when backing up to usb disk with boot partition on it

You just installed your shiny new SSD into your laptop.  The obvious use for the old hard drive is to put it in a cheap $10 usb case and use it for backup.  However, I have found on several occasions that Windows Backup will not complete the system image portion of the backup.  There seems to be a bug in Windows Backup that causes it to fail when there is an EFI and/or Windows partition on the target drive.  Screen shots below -

Click "More information" button to see Error 0x807800C5

Backup disk has an EFI partition

To solve this problem, it is necessary to remove the EFI partition.  It can't be done in Windows Disk Management, so the easiest way to do it is DISKPART.  More to come on that later.

I also tried this in Diskpart

  1.  Select volume <vol>

  2.  set id=ebd0a0a2-b9e5-4433-87c0-68b6b72699c7

Here is part of a post I logged with in this issue in the Microsoft forum

http://answers.microsoft.com/en-us/windows/forum/windows8_1-performance/windows81-pro-system-image-backup-cause-error/88bcede8-eb0d-46d8-ac73-187720f4ce2e

This is not fixed.  I have just installed 2 laptops with fresh copies of Windows 10 and all the updates.  These laptops each started with an empty hard drive and after installation and updates are on Version 1511, OS Build 10586.218.  In each case I installed a new SSD the laptops and in each case I put the original hard drive (which had a different copy of Windows on it) in a USB case and tried to run Windows Backup to the USB drive.  The system image portion of the backup does not complete and the error code is 0x807800C5.
The only way I solve this error is to delete the EFI partition on the backup drive.  The problem with that is that I don't want to do this because I would like the option to put the original drive back into the PC to go back to the previous version of Windows if I need to.