How To Manually Upgrade Windows 10 Mobile?

What if I went back to Windows 8.1? I don't think this phone was in the Insiders program.

There is no other way for this phone to be running on an unsupported build, as it is running a version of Windows 10 Mobile version 1709 build 15254 / Fall Creators Update, for which the 1520 was never supported.****

If you go back to 8.1 you can only update to the current version of Windows 10 Mobile version

 1607 build 14393 / Anniversary Updatefor which the 1520 is officially supported and your second device is running. Official support for this OS build ended on October 9th this year, so it would seem v10.0.14393.2551 is the last and final release.

There is no longer access to the Insider preview versions of Windows 10 Mobile version  1703 build 15063 / Creators Update and Windows 10 Mobile version 1709 build 15254 / Fall Creators Update.

What if I went back to Windows 8.1? I don't think this phone was in the Insiders program.

What then prevents Update from updating the phone to the version of the other phone?

Your first one is running an Insider build which it received while the program was still active. Your second one is running the latest available officially supported OS build. You cannot upgrade from that to an Insider build, especially when it is no longer available.

What then prevents Update from updating the phone to the version of the other phone?

I have two identical Lumia 1520's. One, which is on 24/7, has v10.0.15254.541 installed. The other, which is typically off, has v10.0.14393.2551. When I go to "Settings > Update & security > Phone update" and "Check for updates" on the later, I am told it is up to date.

I realize that Windows Insider Program has stopped "In Flight Upgrades" for devices with versions <=v10.0.14393. How can I manually upgrade this phone to match its partner's version?

The Windows Insider program for Mobile ended back in January, there are no new builds to be released. You cannot manually upgrade your second phone.