I was having the same problem and stumbled into a simple workaround. I'm not sure if this solution is bug-free, but it's working for me. Basically combine the two methods you started with, calling the function with spoofed eventdata and immediately resetting the SelectedObject so that it matches. You can reset before or after you call the function, as long as you pulled the previous value to use for the OldValue in the spoofed eventdata.
As far as I can tell, calling the function gets you all of the results of an actual event while ignoring SelectedObject and manually changing that doesn't have any follow-up effects.
I also tried to use notify() but all I got was: No method 'notify' with matching signature found for class 'matlab.ui.container.ButtonGroup'.