Oh, dear. I very much sympathize regarding the misinterpretation of terms as I have done similar things in the past where I found out, much to my chagrin, that certain grade-related terms did not mean what I thought they meant in the country where the functionality was developed (In other words, it was a moment of, "Huh, I guess that does not mean the same thing in Australia as it does in the U.S. Who knew?").
That said, at first I thought it was mostly just a language issue that could be refined by just better naming conventions. Then when I tried out your scenario for myself, I did really wish that whatever the cutoff date functionality is called (it is really the final, absolute due date), I could use it without having to set a due date, per se--meaning that from a user perspective, I do agree that it would make the most sense to have the ability to set the cutoff date as the date that shows up on the assignment info page communicating to students what is due and when and that if it could be set without a due date, it would essentially BE the final due date. Not sure how that would work or if it would be possible to do without causing havoc in the code.
It is good that you have brought up this issue here as now we can find out more about what is possible from those who know the code, explain the basic requirements for the change, and then have someone take the pertinent parts of the discussion to the Moodle Tracker where we can have the nitty gritty functionality/feature change request discussions with the developers. In addition, from there votes will tell them how many of us who use the module think this would be useful.