Here's how I solved the Mac backup problem.

Wiped the big new disk, fresh-installed the latest Mac OS on it (Sierra).

Booted from the new disk.

Downloaded and installed the software I need to run my world. Chrome, GitHub, Atom. Copied the OPML Editor from the previous boot disk.

Installed Dropbox and logged in. Let it populate. This is actually a much bigger step than installing the OS. Hopefully it'll be done by tomorrow morning. In the meantime I can use the machine.

When it's done, I'll turn on Time Machine with an empty fresh disk as the backup device.

Eventually I'll wipe the old internal startup disk, assuming everything goes well.

The mess that is Mac

Ever been to Penn Station?

It used to be a majestic structure, a train station from the age of trains.

When a city's rep was a function of the majesty of the station.

Then they decided majesty didn't matter, and they decapitated it. Removed the majesty and kept the trains.

The Mac OS is kind of like that. I don't remember Penn Station before it had its head lopped off, but I do remember the Mac.