I am confused translating "klingonness" (Quality of being Klingon, akin to Humanity). I understand that there is no such thing as an abstract noun affix from a noun in Klingon and that tlhIngan is a noun and not a adjectival verb (i.e. to be klingon –I find it odd there isn't), so *tlhInganghach is wrong.
tlhIngan Dotlh (Klingon status) seems lacklustre and tlhingan chaHghach (klingon being) is most likely wrong, but I am not familiar enough with Klingon to think of a noun that fits the bill.