Sims 3 - "There is a problem connecting to the server..." installation error

As Bluebellflora described, TS3 is refusing to run on my mac.  I received a message of a successful installation, and the launcher loaded properly.  But when I pressed Play, the game hung on the plumbob screen that immediately precedes the black screen/intro sequence.  No matter how many times I tried, I'd eventually get the error message captured in the second screenshot above.  This was true whether I opened the launcher or bypassed it.  (If I launched the game while disconnected from wifi, I got the first error message above.)

When I opened the launcher, I had a single plumbob in my dock, but after pressing play, a second one appeared and remained unless I force-quit it.  (Unfortunately, doing so didn't help the game get past the plumbob screen.)  I also had two Sims 3 entries in my Activity Monitor, each with distinct stats:

For the record:  I started by running the uninstaller, and then I followed Bluebellflora's guide to manuallly uninstalling TS3 and removed all traces of the game from my computer.  I only reinstalled the base game, no packs.  I also removed all game folders (in Documents) as they were generated during troubleshooting.  At one point, I uninstalled the game again, then did a clean uninstall of Origin as well.  Nothing helped—the same error messages showed up no matter what I did.

I've played TS3 on this mac since I bought it in December, and other than the issues with installing certain problem packs (easily fixed by Bluebellflora's guides), I've never had any trouble running the game.  My specs (below) are more than sufficient to support every expansion pack, and I'm still running Sierra, the OS that came installed on my computer.

Mac OS Sierra

MacBook Pro (15-inch, 2017)

Processor: 2.9 GHz Intel Core i7

Memory: 16 GB 2133 MHz LPDDR3

Graphics: Intel HD Graphics 630 1536 MB

                AMD Radeon Pro 560 4096 MB

Storage: 512 GB SSD