Am I right and the difference between unceasing and ceaseless (for example, attempts) is that
the first is more likely used when smb. does something – does, does and does - being guide by some his/her internal motives and despite everything :),
whereas the latter is more probably used when there are some external circumstances that make no hope for successful ending for that
Or it’s just my, yet another, cranky thought and wrong listening/understanding, but in your real use of the words there is no (such a) difference?