Note that IMO the primary tone color you get from the MM is the Maj7 chord and note, rather than the dominant 7.
Here's a Melody Maker layout:
Hole: 1 2 3 4 5 6 7
8 9 10
Blow:[Eb G C Eb G]
Bb[Eb G] Bb Eb
Draw: F [Bb D F A]
C [D F A] C
And a Natural Minor layout:
Hole: 1 2 3 4 5 6 7
8 9 10
Blow: C [Eb G C Eb G]
C [Eb G] C
Draw: D G [Bb D F A]
Bb[D F A]
The brackets '[]' and coloring show where the notes are the same. Since the MM only modifies the first what-would-be draw C to a Bb, the other 2 C's on the draw don't align with the Bb's on the NM. On the blow side there's the same Bb/C mismatch, but much the rest is the same after NM hole 1.
So, the Maj7 chord on the MM--the Bb D F A in holes 2-5 draw--is right there on the NM in holes 3-6 on the draw. The Natural Minor actually has the Maj7 chord again! More than the MM... And, the Major6 and minor chords on holes 1-6 of the MM are there on the NM as well. The major chord on the high end of the MM is a minor chord on the NM...
Anyway.. the point is, there's a lot of overlap between the two tunings. Much of the flavor of the MM can be found on the NM. AND, every chromatic note except one--the Gb (flat 6th)--is in the middle Bb scale (so-called by Lee Oskar 3rd position) of the NM tuning. (The Db, E, Ab, and B require normal draw bends.)