Yes, that little book packs a lot of dynamite, doesn't it?!?!
Let's talk a little about chord forms 4 and 5. First of all, remember that Mickey's fingerings were for a plectrum guitarist that only had a single pick to strum a chord. I believe he chose fingerings that allowed the guitarist to deaden unused strings so that when you strum through the chord, the deadened string wouldn't sound. Also, he gives us 4, 5, and 6 note chord forms. So often we can omit the highest string or couple of strings.
Mickey fingers that Chord form 4 (a minor 7th form) with the 2nd finger on the 6th string and a barre on the top 4 strings by the 3rd finger. Note that in both of those chord forms the 1st string note is a two octave higher repeat of the bass note on the 6th string. What your ear concentrates on is the bass note and the movement on the 4th string, primarily. The other notes are heard, but it's that movement that builds the interest. Let's omit the 1st string, and use the 3rd finger on the 4th string, 4th finger on the 3rd string, and if you need to have the sound of the 2nd and 1st strings, use your 4th finger for it. The to go from a form 4 to a 5, just move your 3rd and 4th fingers to the 3rd and 2nd strings and put your 1st finger on the 4th string, one fret lower. The key to accuracy, I believe, is maintaining the 2nd finger on the 6th string as an anchor note.
The concept of an anchor note to move from one chord form to another is almost a "golden rule of chording." Many great guitarists have commented on how it improves accuracy.
Those of us that play fingerstyle can just make a 6 string barre and just not play the 5th string, or play a note on the 5th string up two frets (which is the 5th of that minor 7).
Fact is, there just isn't 1 fingering that is appropriate for all instances, and as you develop you'll probably come up with a number of different fingerings for that chord and use them all. Personally, I probably play that chord while comping 75% of the time as a three note chord using the 6th, 4th, and 3rd strings only.
My personal hero of rhythm guitar playing is the great Freddie Green of the Count Basie orchestra. Freddie often used just 2 and 3 finger chords, but kept a rhythm with the accuracy of an atomic clock. If you can find some Count Basie albums, listen to Freddie's playing.