When is the best time in the Northern Hemisphere to sow new seeds, in the fall? (Outdoors of course, I don't plan on starting any more batches inside, I will keep my inside gear solely for if I decide to try growing more tropical species, that need to be brought inside during the winter snow, or I might look into building something outside for those species)
The best time is right after they fall. Some seeds maintain viability just a few days after they fall off the tree, and they expect warm weather and cold weather on the regular schedule. You read about stratifying seeds, etc., but that is just an attempt to make the seeds think winter has happened.
Let the seeds come off the tree, put them loosely covered in some soil, and let them grow. They probably won't all grow, and that is nature in action.