distinction between noun forms

Is there a use for the words skillfulness, lustiness, reproachfulness, greediness, allurement, angriness, brawniness, and sorrowfulness?

Each of these is in Merriam Webster without comment under the corresponding word without the -ment or -ness suffix.

Do these words communicate something that skill, lust, reproach, greed, allure, anger, brawn, and sorrow don't? "He demonstrated great skillfulness" seems merely a clunkier way of saying "He demonstrated great skill." Are there situations where the two forms have a useful distinction?

The words are different indeed.

Consider skill versus skillfulness.

Let's have a look at the base word and both suffixes. We start with skill:

skill: The ability to do something well; expertise

The suffix -ful, when applied to nouns means:

-ful: full of

1.1Having the qualities of

The suffix -ness always describes a state of something:

-ness: Denoting a state or condition

So of course you can say both:

The ninja's most important skill is mastery of stealth. &

The ninja's most important ability is being skillful at stealth.

Both sentences are more or less the same, the second using and adjective where the first uses a noun. However you cannot say:

The ninja's most important skillfulness is mastery of stealth.

It would mean the the ninja's most important state of having a skill is mastery of stealth. That does not make sense. Thus, you can see, both nouns are not generally interchangeable.

That's also your answer, the nouns you ask about confer information about the state of something. Mostly the base nouns do this as well to a certain degree. The other way around does not work as I showed above. If the rest of your sentence doesn't fit if you are describing a state or condition of something don't use those words.

Words are imprecise. There are ways in which these words can have different meanings.

You exhibit an amazing skill. (Something like woodworking, cooking, etc.)

You exhibit an amazing skillfulness. (A quality of having skill, not a particular skill.)

Don't offer me your reproach. (That negative thing you want to say, don't say it.)

Don't offer me your reproachfulness. (Your quality of negativeness, not a particular negative statement.)

So it seems in general the -ment or -ness words are about a general quality, and the base noun is or can be about a specific instance of it. (Though the base noun can be the generalized quality.)

An exception is lustiness, which is the state of being lusty (full of life and vigor), not the state of lust (desire). I'm also not seeing a meaning for brawn distinct from brawniness, either.