I wouldn't consider what you need to do as 'down grading'. Instead, leave 10.3 alone, then download 10.1 from More and install it on your boot drive, being sure to rename it during that process. Live large.
And not to say this will be clean, just perhaps your best approach given your goals.
- Once opened in a higher version Xcode, a project is liable to complain if you try w/earlier. Open it in Xcode 10.3 first, setting compatibility lower so it won't complain when you open it w/10.1
- Multiple versions Xcode will all use the same prefs. plist, so certain things you do in one will be reflected in the other.
- Be sure to option-clean the build folder right after making changes, and after switching from one Xcode to another.
Thanks so much!