Chosen Solution
My mini is a unibody mid 2011 that won’t install Mojave. Will the logic board for the late 2014 fit? The external footprints are the same, but I don’t know about the internal (logic board itself) footprint.
No, unfortunately. You cannot use a 2014 logic Board in a 2011 due to port and connector differences. However, if you are a brave soul you can try DosDude1’s macOS Mojave Patcher to install Mojave on your Mac mini. http://dosdude1.com/mojave/