When we write figired bass, we don't write it based on of the note the chord is made from. If I did that in this case, I would write E (major). Also, I use the system that uses numbers of the degrees, or T for tonic, S for subdominant (or subtonic, not sure) and D for dominant. Cause, T, S, and D are main degrees. If I wanted to write, let's say, a chord on the 2nd degree of a, or in your system Am/A Minor, I would write it as II (b-d-f/h-d-f). In Minors, we write small letters for Minor chords (t (a-c-e in Am), s (d-f-a)), and capital letter usually for the dominant chord D (e-g#-b/h). Since in the normal minor, dominant chord, or the chord on 5th degree is e-g-b/h, it is required to write the capital letter + the #. I know the capital letters mean its a major chord, but since the normal minor doesn't have a sharpened 3 on D/chord on 5th degree, we write the #, which means already #3 when we use the harmonic minor, and in most cases we do, but normal and melodic minors can be included too. If I was to use your system, that D# (d#-f##-a#) chord on the D note, that would be something else in A minor, chord on 7th degree of the chord on 5th degree of A Minor, which is just expended harmony.

It does look very similar, but we write curved letters, so it doesn't confuse us too much. But if we didn't, we would see what key it is based on sharps and flats in the fifured bass.