I found this add-on: align by faces (just select both faces in edit modes, then shift-select both objects, then click a button): Align objects by faces. (or github: https://github.com/trethaller/blender-addons).
It takes about 5-10 seconds if you know what you are doing.
Hope it helps.
Demo video: https://www.youtube.com/watch?v=DvVD2Eb7LfI