May I make the following comments, if they have not previously been made by others. Hopefully this will not all be old news.
My studies are limited to Paris quadrifolia and P. polyphylla only.
Both of these seem to follow the very familiar germination pattern of Trillium grandiflorum. That is to say, when cleaned and moist packed fresh after collection and kept at warm, germination occurs the first season, anywhere from 4-6 months (radicle only). A cold period is then required for first leaf emergence (hypogeal).
If one had the proper facilities to keep them at warm until mid to late fall, and then provide cold, one could certainly get these species through their first stage to cotyledon emergence fairly quickly (as is being done with Trillium grandiflorum by some growers).
I have now repeated the Paris quadrifolia experiment three times, with exactly the same results. And germination at the warm phase is quite phenomenal (I would say over 90%). So, Paul, when you said you had germination over a 6 year period, I would explain that as inconsistent moisture and temperature regimes over that long period. My zip lock bags are kept at fairly consistent moisture and warm temperature levels throughout the period of moist packing.