I don’t see the relevance of a pilot “nominating” the crossing runway to the operation of 91.370(3)(c). It seems to me that the operation of that provision depends on the timing of the landing on the crossing runway. I suppose that if a pilot chooses to use the crossing runway and nominates a time of landing that is before the planned take-off of the ‘subject aircraft’ and that timing is correct, the pilot of the latter must comply with the requirement in (c).
Back to basics: These non-controlled aerodrome rules were originally designed to work without the benefit of radio. You look out the window of your aircraft to see whether there’s anyone on base or final for or on the runway on which you’re about to line up and, after lining up, you look to see whether there’s anyone on base or final for a crossing runway. And if, for example, there’s someone just about to touch down on 27 and you’re sitting on the piano keys of 36, best to wait. (BTW: An ATC friend advised me to do the same thing at controlled aerodromes, just in case ATC has stuffed up…)
General point: These rules are originally based on the maritime collision regulations. Crusty old maritime regulators will tell you that if there’s a collision between two ships under way, it follows that both masters have breached the COLREGS.