Gerhard, using a more robust search for the black point (20 trials with random starting points) on your data set results in the following:
XYZArray: No. elements = 1 0: 0.018478, 0.018829, 0.015137 [Lab 14.860508, 0.784551, 0.455625]
xicc/xicclu -ip -fb -pl CHP410-1200.icm 0.000000 0.000000 0.000000 [Lab] -> Lut -> 0.999641 0.101813 0.132937 1.000000 [CMYK]
Note that Lab 0 0 0 returns the closest point from the perceptual table, not the black point. Profile chooses the black point to be the lowest L point within the gamut with the same direction as K only. (This seemed a reasonable thing to me, since K only is often used as a reference black hue within CMYK systems.) There may be points in the gamut with a lower L, but they may have a not so neutral color.
xicclu -ia -ff -pl CHP410-1200.icm 0.999641 0.101813 0.132937 1.000000 [CMYK] -> Lut -> 13.500272 0.608876 -3.316293 [Lab]
Which is consistent with what profile found. Does this seem a better result ?
[Thanks for drawing this problem to my attention.]