https://docs.joomla.org/Build_Test_Packages_From_A_Release_Branch

Thanks, done.
But, how do I trick Joomla into accepting a core update package from a local URL (or file)?
I have used Options to get to the Joomla! Update: Options screen, have set the Update Channel to Testing, set my custom URL (where I have the Joomla_3.7.0-beta1-dev-Update_Package.zip file), but I still cannot update.
I have also tried using the Custom URL option without luck.
I have created my own list.xml & extension.xml (including with _test in the xml file names).
After I clear the cache, I get a warning that my list.xml cannot be opened (site #1 "Joomla Core"), even though I can access it by copying the url into a browser tab.

It's not happening and I don't know what's going wrong.

Components -> Joomla Update -> "Upload & Update" tab -> Select your zipfile and hit the button. That should do the update.

not a bug

I don't have a "Upload & Update" tab in the 3.4.8 version I'm upgrading from.

Yep, that doesn't exists in that version. Try updating from a 3.6.5.
YOur 3.4.8 installation should be updated to 3.6.5 anyway.

I updated to 3.6.5 and that has the tab. My 3.4.8 install is on a dev server virtual host that I could sacrifice.