i don't really understand how one can recommend a shutter speed to use, given that exposure will always be different. this is a fixed aperture camera, so if you have to use 1/60 for shutter speed, that means that the auto ISO must be in play, right? In the case of your 1/60 shutter speed examples, the shots are clearly over exposed, and all sky is blown out. that will always result in a loss of image, however good the LUTs are. Did you see from the histogram whether it was clipping on the right?
what would be more useful, to my mind, would to have some settings where the exposure is 'correct' but the contrast is reduced by a set amount (presumably what LOG mode is for). then you know you're not blowing out the highlights, and the darks are raised. then the LUT has something to work with.
On my screen the one I preferred was the auto setting with contrast and saturation -3, with the LUT applied. Did you happen to shoot in auto/LOG mode by any chance?
Unless I'm missing something, the only reason for Neumann Films to determine a shutter speed to use is so that the auto ISO would be as low as possible, resulting in the least amount of video noise - but it appears the ISO didn't go low enough in your 1/60 examples.