First, if using a manufacturer's LUT for normalization, apply it via the Creative tab LUT slot, NOT the Basic tab!
Second, do NOT use the Blacks tool in the Basic tab to drop your Shadows darker. It will cause banding if you do. It's only useful for a few points of change of the actual black point.
Why for both? I'll start with LUTs.
Colorists call LUTs the "dumbest math out there" for a reason. There's no subtlety to them, they're a simple math table matrix operation. X pixel becomes Y. And built on an ideal exporuse in an ideal lighting setup for contrast and saturation.
Field produced media rarely matches the exact lighting/camera setting combination of the LUT creation process. So ... you need to be able to apply the LUT, then trim the clip's exposure ... the white point, black point, contrast, and saturation ... "into" the LUT while viewing the image and the scopes.
In Resolve, you apply a LUT to a node, it's processed after any changes you make via the color controls in that node. This is correct. Premiere's Basic tab ... isn't. They're even thinking about changing that processing order, putting the LUT after the controls.
So apply the LUT in the Creative tab, trim all the tonal controls in the Basic tab, it will work better.
For manual normalization, here's my suggestions. Including why the Blacks tool is so limited.
First ... the Contrast control is the best for much of the needed expansion, BUT ... it always is based on expanding outward from the 50 nits middle of the RGB Parade/Waveform scopes. So use the Exposure slider to move the signal in the Waveform scope so the the middle of it is centered on the 50 nit left side marker, then use Contrast to expand evenly below and above that 50 nit marker.
For fine tuing the white point, the White tool is more specific than the Exposure tool. The Whites tool is like grabbing the right end point of the RGB Curves tool and moving it around. The Exposure tool lifts everything, but ... it's like grabbing the middle of the RGB curves and lifting. Stretching out the Shadows, compressing the highlights up to the white point.
For shadow and highlights area fine tuning, work the Shadow and Highlight controls.
Do NOT use the Blacks tool for anything other than a 2-5 point shift in black levels! Just ... DON'T!!!
The Blacks tool is rather odd, it's like a swinging gate/door at around 12IRE/nits. It will not affect the clips above that, so it simply creates banding if you use it to move shadow data down.
So use the Shadow tool to set your general low values, and only use the Black point for a very minor change.
Neil