Your negatives are fine. The film seems to be capturing exactly what it is supposed to. One advantage of negative film over a digital sensor is the softer saturation characteristic. With a digital sensor, when brightness goes past the sensor's upper limit, the values hard-clip. Negative film doesn't clip at a fixed hard limit, but saturates over a range.
You seem to be getting what you should from the process of inverting the scanned negative data to make a positive. Much of the scene information is captured, which is really all you care about going into post-processing. It doesn't really matter at that point whether it's high or low contrast, since that is something you can adjust in post-processing.
The lighthouse picture is a great example of that. You made the contrast much higher. Personally, I think too high, but that's of course totally up to you. Still, you got what you wanted. There doesn't seem to be a problem here.
For example, here is your second picture after just the original inversion:
And here it is after some adjustment to the colors and contrast:
Personally, I think the second version looks better. Many other results could have been derived from the original inversion. That's really all you need from your raw pictures: The ability to derive what you want in post-processing without introducing artifacts.
Note that this also points out difficulties with a film process. The film reacts non-linearly to brightness, and each of the color layers respond differently. This means you get hue changes with brightness.
The second version looks to have more natural colors overall, but there are parts that still don't look right. I wasn't there, so of course can't say for sure, but color balance of the rock wall doesn't look right to me. Other parts of the picture look reasonable.