Here's what fixed it for my Brother HL-L8360CDW printer. It looks like the problem is with the "Brother Generic Jpeg Type2 Class Driver". I installed the Brother driver: "Y16D_C1-hostm-130.EXE". The problem here is that this EXE doesn't actually install the driver, it just uncompresses the files. You have to find: dpinstx64.exe and run that.
Go to "Settings, Devices, Printers & scanners", click on your printer and click "Manage". Click "Printer Properties" and select the "Advanced" tab. Make sure the driver is the one specific to your printer. In my case that was "Brother HL-8360CDW series". Click on "Printing Defaults" and a more elaborate option menu pops up. A little more than halfway down there is a "2-sided / booklet" drop down. Select "2-sided" then below it click on "2-sided Settings(X)" and select the "Long Edge (Left)" option which will actually affect the printer behavior.
Hope this works for everybody.
January 2019 update.
There are new versions of the Brother software suite (A2) and the driver (1.40) available on the Brother support site https://support.brother.com/g/b/downloadlist.aspx?c=us&lang=en&prod=hll8360cdw\_us\_eu\_as&os=10013 . I also found installation instructions: https://help.brother-usa.com/app/answers/detail/a\_id/120508 . The new driver file is Y16D_C1-hostm-140.EXE. The hack above still works, but you are probably better off following the instructions.
To everyone who thanked me, you're welcome -- especially the person who nominated me for sainthood!