Your right 9th, 11th, and 13th chords are not labeled as minor or major. The 9th chord is really a 2nd, which is both a major 2nd above the root in both major and minor chords. 11th chords are perfect 4th's above root. 13th chords from the discussion about major and minor 6th, we know that a 6th is always a major sixth above root in both major and minor chords. 9th are common to alterations, whether flattened or raised in blues context (dominant 9th mostly). The 11th chord has one alteration and it is extremely rare. Some times it is raised to maj#11. This is natural on the IV chord in a major key. In C major, F to B is a #11 or #4. Again it's rarely used, but when so the #11 is looked at as a leading tone, B-C. Make sense.

When playing 13th chord, there has to be a compromise. 7 notes, 6 chords. It's better to drop either the 11th or thr 5th. You must keep the 7th and 3rd. The 9th is truely optional, throw it out when the chord sounds to strong. You can't drop the 3rd because then you don't know whether it's major or minor. You can't drop the 7th because then you could be left with a (maj/min)6/9 chord.

If you playing in a jazz band, it's not uncommon to leave out the root and just let the bass play it. That might help also, but check the sound to make sure. In jazz the bass won't stay on the root for very long so that might be a problem.

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