And BTW, just looking at your Hard.cube file, that’s a very weird LUT, it just looks really bad.
$ gmic Hard.cube
It has an almost complete black plane for G==0 and a complete white plane for G==1, with a lot of negative values between the two. Looks like non-sense to me 
If you look at the content of the .cube file, you can see it does not start that well either:
$ more Hard.cube
LUT_3D_SIZE 16
-0.097565 -0.092976 -0.097565
-0.098757 -0.094101 -0.098757
-0.081556 -0.076978 -0.081556
-0.083550 -0.078564 -0.083550
-0.105227 -0.109099 -0.105227
0.069769 0.065046 0.069769
0.120758 0.139960 0.128572
0.217449 0.231766 0.223222
0.316694 0.328851 0.309323
0.403193 0.397478 0.383101
0.435610 0.450181 0.422819
0.468827 0.464416 0.444418
0.483378 0.481327 0.456084
0.486645 0.489613 0.468634
0.519337 0.513052 0.485468
0.627504 0.616512 0.591214
-0.098685 -0.093574 -0.098685
-0.098884 -0.093653 -0.098884
-0.078577 -0.073320 -0.078577
-0.088576 -0.085038 -0.088663
-0.115649 -0.122366 -0.115763
0.053534 0.044668 0.054072
0.107927 0.126797 0.120761
0.218742 0.224018 0.219249
0.311826 0.321831 0.301112
0.400291 0.395240 0.380709
(...)