I don't know Steve's Luts, so let's just stay with the Resolve REC709/2383 preview LUT.
Yes, if you are grading through this LUT you will need to adjust your original Log footage to make a pleasing image through this LUT. If you have your 2383 preview LUT in the middle of your node tree, than you can make further corrections after the LUT if you wish, using traditional Lift, gamma, gain controls.
If you are not pleased with your results using this LUT to de-log your material (assuming it's Log in the first place!), you can use a LUT provided by the camera manufacturer. This will give a much more neutral representation of your image than the 2383 preview LUT.
But you do not need to use any LUT at all, or, as I sometime do when I want a bit of the "film look" I use the 2383 LUT set at maybe 30% effect. And even at 30%, I need to grade for this LUT.
In your case, you are using a tool that is designed for making a film negative in a workflow that is not making a film negative. You are not "doing something wrong" that makes the green colors unpleasant. If you see unpleasant colors when you use the LUT then, don't use the LUT, or you will need to grade for this LUT.
There are also LUTs that take an existing REC709 gamma 2.2 image and simulate a film print. But they are derived from the preview LUT and might not make you really happy either. But, you could apply this LUT at just 25% or something like that and get a filmish "feel" without going too far off base.
I really think that if you really want to start with a kind of normal image, from LogC camera original, than use one of the manufacturer's LUTs and start with that. I know that Marc likes to do the basic color matrix correction himself by eye, but, from my experience, I like to start with the manufacturer's LUT and make it wrong by eye from there (to my tastes of course!)
If you like what you're doing with the 2383 LUT and making your corrections for it, than you can keep doing that. But I think eventually, all your work will have the limitation of this "look" and you will want to try something different.