Thanks for reporting back on this. Classy. I'm sorry that you had to suffer in silence here. Some thoughts:
1) The place I see this come up most is with temporary works beams. There, I've seen some charts that deal with this by designing the beam for LTB assuming an exaggerated length to account for the lack of support restraint.
2) You'll want to have one of our antipodean friends fact check me on this. Some time ago, I was involved in an LTB thread per the Aussie code. My recollection is that their LTB methods do take some account of the rotational support conditions.
3) I've been checking this condition using side-sway web buckling per AISC in many practical situations. I feel that is quite salient and speaks a bit to the "web distortion" issue mentioned in the abstract for the paper that you referenced.
In your situation, is the top flange restrained at the supports?
I believe that using appendix six would require one of two approaches, both of which introduce annoying complexity in my experience:
4) Assuming that the column, and it's connection, torsionally bracke the beam or;
5) Assuming that the compression flange itself braces the beam as a sort of girt.
If you've evaluated this, can you describe the method that you went with?
If you feel that "the moment has passed" on this, don't feel any pressure to respond to my questions. That said, if you remain interested in further discussion, I'm game. Your ongoing contributions here entitle you a seat in first class when it comes to having your own questions discussed. If I can help, I will.