Well for starters using roman numerals is bad because in this particular case i read VI7 as you wrote (in A minor as you were using) as F7 not Fmaj7.
The same goes for the i/VI that you wrote, i read this as Amin/Fmaj (An A minor chord over a F major chord). If you were to write to show something being in inversion and being in the bass, for that chord you would write VI6 to indicate that it is in first inversion.
You're better off explaining a progression with chord symbols rather than Roman numerals because of the ambiguity that will come out of using the symbols that way.
So to answer your question op, the progression is probably better off explained with Fmaj7, G, Em7, Am; rather than Roman numerals.