Correlating the Four Temperaments with Myers-Briggs

I've seen charts galore that correlate the various personality systems with each other, and while I do see patterns (I'm all about patterns), whoever translated David Keirsey's four temperaments (derived from the Myers-Briggs) into the classic four temperaments (melancholic, phlegmatic, sanguine, choleric) must have wanted it to fit in a neat package, and I don't think it does.

The charts I've seen show this:

NT=Melancholic
NF=Phlegmatic
SJ=Choleric
SP=Sanguine

Does anyone not see the glaring problem here?   The classic types are based on introversion and extraversion.

Melancholic, Phlegmatic = Introvert
Sanguine, Choleric = Extrovert

My research and experiences with both systems has resulted in major mind spinning analysis, only to come up this obvious and simple conclusion, which basically says that the classic four temperaments describe how we relate to the world (first and last letters of the Myers-Briggs types):

IJ=Melancholic
IP=Phlegmatic
EJ=Choleric
EP=Sanguine

Who are the controlling types?  The cholerics and melancholics (I know because I am the latter, of the NF variety).  Who are the laidback types?  Sanguines and phlegmatics.  Or to use Gary Smalley's original terminology:  The beavers and the lions are the intense Type A personalities, while the otters and golden retrievers are light and fun loving.  That's not to say they don't have depth/passion--they definitely do but it's expressed differently--that's where Myers-Briggs personality typing fills in the gaps, i.e. the two letter void in the middle that says oh-so-much about our personalities.