When the problem first developed, I sent the output to the boot-utility folks also. It was a while before they got back to me, plus I didn't get back to them immediately because I felt I would probably find something in the Internet how to make it work. I didn't, so I followed up with them. First they had me do the following:

hello Don,
Please: 
1) run Boot-Repair --> "Advanced Options"--> untick "Backup and rename Windows EFI files" --> tick "Restore EFI backups"  --> Apply, and tell us the new URL that will appear.
2) reboot the computer and tell us what you observe

Regards
The B-R team

This was my reply to them with the results  after doing the above:

Hi,
Thank you so much for your help. We progressed, but aren't done yet. I have windows booting now as it normally would. The grub options didn't show up at all now. Here is the log:
http://paste.ubuntu.com/7318099

Thank you again so much.

Then they wrote back and had me do the following:
Hello Don,

Good job :)
Now please go into your BIOS (UEFI firmware ), and select "Ubuntu" as default boot entry in the boot order menu.
If unsure, please send us pictures (taken with camera) of your BIOS menus.

Regards
The B-R team

Here was my response to trying that (I had pictures in the e-mail back to them.):
Hi,

Thank you!

If I press F12, I have the option to select what I want to boot from. However, all I can do with this menu is to select. Even though there are the up and down arrows and it says to move selection, if you try to select any of them so you could try to move them, they automatically execute. So I can't move Ubuntu to #1. If I don't do anything when the computer is in the process of booting, Windows boots. If I select windows from the BIOS menu, windows boots. If I select Ubuntu, I get the Grub menu where I can select Ubuntu, Ubuntu advanced, and Windows. It does not include the Windows restore link.
If I select Ubuntu in the Grub menu, Ubuntu boots. If I select Windows in the Grub menu, Windows boots. 
I went into the BIOS (Yes, I do know that isn't the proper terminology. I guess I'm set in my ways.) I could not find anything directly in the BIOS which would let me change the boot order.
​
In order to change the Boot Mode or Priority, I had to enable CSM. In Boot Mode, I changed it to UEFI first from Auto. I also changed the Boot Priority to UEFI first. I saved the settings and rebooted. The computer would not boot. I went back and changed them to the original settings, and everything works as described above.

It seems to me if we get the BIOS to recognize GRUB, then we should have a working situation, but I'm the amateur and you folks are the professionals.

Thanks again for all of your assistance.

Don

I've attached the complete e-mail with the pictures. On one hand, I would really like to have this fixed. I do 95% of my work in Ubuntu, and having to hit F12 all the time when I boot to be able to get into Ubuntu isn't efficient use of my time. Plus, I might wear out the F12 key! But, at least after a month, I can get into both systems. It seems like there are lots of problems. It seems like Ubuntu is getting a lot of blame for the issues, but it all goes back to Microsoft and their efforts to mess up Linux. So far, they have succeeded.

I'm still waiting for a response from the boot-repair folks on what to do next.

Don