After making my original post, I realized that my MacBook Pro's fan would kick into overdrive whenever I attached my camera. I pulled up Activity Monitor and found that the "icdd" process was chewing up a large amount of CPU. "icdd" is the ImageCapture Discovery Daemon and, according to the documentation, "icdd is a system daemon responsible for matching devices containing images with the appropriate driver modules." There isn't much information out there about troubleshooting icdd, but I did find a posting from 4+ years ago on Stack Exchange that asks about this very issue.
The solution that worked for me is in the most upvoted answer. To sum up, you have to log off, log on as a different administrative user, and delete your deviceInfoCache.plist file. In my case, that file was 80 megabytes!
In more detail:
First, make sure that you have another administrative account on your Mac. If not, go to System Preferences, Users & Groups, and create one. It must be an administrative account!
Next, log out of your account completely and log into the other administrative account.
Next, start the Terminal app. You can find it by going to the Applications folder and then the Utilities folder or by pressing Command-Space and typing "Terminal".
Once in the Terminal, become the root user:
sudo su -
When prompted, enter the password of the administrative account you're using now.
Next, you have to delete the deviceInfoCache.plist file for your regular account. You'll need to know what your shortened username is. If you don't know what it is, then go to the Finder, click on the "Go" menu, and choose "Go to Folder..." In the pop-up box, enter "/Users". You'll see a list of the home directories on your Mac. Your regular user's home directory should be fairly obvious. The name shown there will be your shortened name.
Now, delete the deviceInfoCache.plist file:
rm "/Users/<your-shortened-username>/Library/Application Support/icdd/deviceInfoCache.plist"
where "<your-shortened-username>" is your shortened username. For example, on my Mac, my shortened username is "chris", so I'd type:
rm "/Users/chris/Library/Application Support/icdd/deviceInfoCache.plist"
Once you've done this, you can quit the Terminal, log out, and log back in to your regular account.
When I did this, my Canon 1Dx Mark II camera was immediately detected by Image Capture, the Canon software, and Photos. The icdd cache file was no longer 80 megabyte, but 1,538 bytes.