@msarrowette For now, I'm going to stick with troubleshooting the iMac, since it's easier to handle one system at a time. And you're right, the game should work fine on both computers, although it would obviously run a lot better on the iMac.
Did you add your graphics card to the .sgr files before or after you tried to play? If it was before, that could be the issue—a stray punctuation mark in the wrong place, or even the wrong type of quote mark, can crash the game. But even aside from that, you don't need to add your card; the game recognizes an AMD GPU on its own now.
So to keep things simple, please restore the original unedited files. If you don't have the original copies, delete the new ones and repair the game in Origin (again), which should put back the default versions. (Please check that they're back anyway, because I don't think I've tested this and am not completely sure Origin does what it should here.)
If this doesn't help, try playing while your computer is offline. You can sign into Origin and put it in offline mode, then disable wifi and/or disconnect the ethernet cable before pressing play.
If that doesn't help either, please let me know whether you run a third-party antivirus or a cleaner app on your Mac, and if so, which one.
I added the graphics card to the .sgr files after the initial attempts to play failed, just in case that was the problem, though I'd have expected an unrecognised graphics card to just come up at the wrong resolution and with low graphics settings. I wanted to try every test I could though.
I then ran repair after the test to revert the game files back to their original state. I did, of course, keep copies of the unedited versions - but repair seemed a cleaner way of putting them back the way they were. I can confirm that the date stamps on the .sgr files reverted to their original date and time after the repair (4 November 2020), so Origin did its job properly.
I forgot to mention it in my original post, but I'd already tried setting Origin to offline mode, and also disabling Origin In Game. I hadn't disabled wifi, but have just tried again after doing that. It still crashes in exactly the same way, I just get an additional "can't find server" on the Welcome page (which is presumably just the Store and the Sims 4 advertising so not an issue).
There's no third party antivirus or cleaner app on my Macs.
Currently testing on the MacBook Air, as the iMac has the 32-bit version installed at the moment so I can play a bit. For now the MB Air has the base game only, so its Intel HD 5000 integrated graphics card should cope. If/when I progress as far as the Sims 3 menu screen I shall switch testing over to the iMac instead. I have all the necessary information to uninstall the 32-bit version and clean up bookmarked for when I need it.
@msarrowette Try playing in a new admin user account on your Mac. Don't sync any data or sign into any other accounts (except for Origin). Don't even use your Apple ID—this should prevent iCloud Drive from interfering.
You can simply sign into Origin and press Play, but if that doesn't help, repair the game and try again. And setting fullscreen to 0 is worth doing again if the game won't initially open; the options.ini file is of course only accessible from the original user account.
New admin account created, The Sims 3.app copied from the original /Users/accountname/Applications folder to the one for the new account since the 64-bit version is user-specific, and then I launched Origin, pressed play, updated when prompted, quit the launcher and then ran repair to validate the game. Then I tried to play.
Alas, I still get the same crash and the same error message.
