And it's "nuachtáin" not "nuachtán" here because... ? (I'm light on the grammar, I know; this is really my entry into Irish.)
… because a verbal noun requires the genitive case in a following noun. (The adjective is also in genitive case, but stairiúil happens to be the same in the genitive case for masculine nouns.)
Scilling has it spot on. In the tips for the Verbal Noun skill, there's a section on "objects after a verbal noun" that includes some helpful examples.