The links for High Sierra 10.13 do not work. Is there an Apple approved source for this software?

The links do work but you must use your Safari browser, other browsers do not work for this.

Open Safari and click on this link, 

How to get old versions of macOS – Apple Support

Go to the Download OS section and click on macOS High Sierra

this will redirect you to the App Store High Sierra download page

it should say Get or Download.

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

Connect your mac to your router via cable rather than rely on WiFi.

Do not use your mac while it is downloading

and do not use any other devices that share the same internet connection.

If the App Store says ‘Open’ then it is detecting a previous download of the install app

go to the Applications folder locate Install macOS High Sierra.app.

Move it to the Trash, empty the Trash.

Restart, click on the link again, the App Store should say ‘Get' or 'Download'.