You sure it was Kodachrome? I thought Ektachrome. I have a stock of the Fuji and Kodak product. It is slow , and needs filtration, but has extremely long straight line response.
The best results are found by testing with a series of varying equalt steps between denisty density white to black targets as the subject. These are found on a macbeth target, or in old darkroom data guides.
Then you read the results with the three colour chanels of a densitimeter, and work on getting the three cuves an equal distance apart on the log plot.
Slope of the response curves is determined by the first developer time, starting bottom point of the straight line part of the curves by exposure, and the space between the curves is adjusted by filtration while taking.
For instance with my Fuji rtp stuff I shoot slide dupes into an MR-16 source at 8" with a bellows, 50mm macro lens and slide duper holder, at f/8 1/30th.
My daylight balanced Ektachome needs 30cc green, and gets exposed on a Bowens Illumitran on full power, balanced needle output at f/8 with a 50mm enlarging lens as the taking element.