I was able to disable the MAME menu by coming in through the Retroarch menu. However, it didn't seem to "stick". Is there something that needs to be done to save the changes once they are made?

I remember a similar post - after the 4.4 image was released - mentioning that DInput behaves differently and switching to XInput made it work.

Thanks that fixed it :)

Also now have a fresh install of 4.4 up and running beautifully.

@myname You don't need to use any config file or modify any file whatsoever. Just follow the documentation and map your controller from Emulationstation, skip the Hotkey button assignment and then choose yes to use Select as the Hotkey button. That's it.

I have now reinstalled the official image on the Pi3B+; did an upgrade (no rpi-update), rebooted. The buttons then didn't work anymore. I then updated Retropie to 4.4.4., rebooted and all is working again. Thanks for your help.