Some powdery substance on roof rafters

Maybe the links have changed, but if this is the product that you were looking at...

then yes, I have had experience with roof to wall vents... they work; but they are for the tops of roofs, where they meet a wall (like for an addition on the side of a house). So, I don't think it would be useful for your house, if I understand your question correctly. If you installed soffits (or found a way to vent without them), then you may want to use a ridge vent (kind of the same thing), but I don't really understand a way around adding/building an overhang in order to have soffits.

I would like to see a pic of your way/solution around soffits (6" vents installed equidistant from each other).

Any moisture issues related to the standing water incident would have manifested itself long before now. Whatever the current issue is, it's unrelated to the previous issue. In that time, it is possible a new leak developed. It's also possible the dark areas are related to interior humidity and unrelated to the roof. In cold weather, the ceiling surface under rafters is measurably cooler than the nearby portion under insulation alone. This can cause condensation only under the rafters. As you know, condensation can lead to mold.

Can you tell if the darkening is due to actual mold? The damp surface can attract dirt that darkens the area even though no mold is growing. Even though the dirt can stain, attempting to clean an area with plain soap and water would yield a very different result than if mold is actively growing.

If mold is actively growing, it is time to consult with a mold professional. They will determine the cause, mitigate the mold, and suggest how to prevent it from happening again. If you want to investigate further before going that route, the only reliable way to determine if the rafters are getting wet is direct inspection.

Cut a small inspection hole where you think it's the worst. If it's wet up there, a lot more ceiling is coming off, so don't bother patching the hole. The roof is leaking. It needs to be repaired and all wet drywall and insulation needs to be replaced. If it's all dry, breathe a sigh of relief. The need to patch the hole is much less than it could have been. Be sure to adequately seal the damaged vapor barrier.

If the rafters are dry, the only thing you can do to reduce condensation on the ceiling is reduce the overall humidity of the house. First try selective ventilation and lifestyle adjustments. Consider bumping the thermostat up a bit. If that's not enough, look into continuous ventilation through an air to air heat exchanger.

A far as replacing stringers, that cannot be done with comp roofing unless a full cold roof is installed. It is normal practice for concealed structural spaces filled with insulation to not be ventilated. It sounds like the roofers followed conventional building practice.