Gee Whiz, your latest post appeared out of sequence for some reason.
And I am certainly not questioning your integrity. Surely there is a right answer and we can arrive at it through rational thought?
I still get 274 even if I do use the track.
I think we agree the track is 170, it is given in the question.
In the specific case where the NDB is at right angles to the track, and on the left, the NDB bearing from the aircraft is 170-90 = 80. In your working you say the NDB "radial" is 260, which is the reciprocal of the bearing from the aircraft, ie 80+180 = 260 so I think we agree on this also.
The aircraft heading is 166 (170 track - 4 wca), I believe we agree on this also.
Arithmetically, the RBI is NDB bearing minus the heading.
RBI = 80 - 166 = -86.
This is a negative number, so we add 360 to get 274.
edited to add:
PS If it helps, I agree that the wording of the original question was not very clear. I also agree with your results for the first two interpretations you looked at. I only disagree with the final "right angles to track" case where you got 264, and I get 274.