When I harvest my seeds, I dry them for a few days in a paper envelope at room temp. After drying, I have stored them in both plastic and paper envelopes in the fridge, this is dry storage. I haven't had a problem with rotting. I guess the seeds were dry enough before storage in the fridge.
A month before I want to be planting the seeds, I put them in dampened perlite in a ziplock sandwich bag or the smaller snack sized ziplock bag. I then put all my baggies in a large plastic bag and put them in the fridge. After about 10 days, I start checking the baggies, and if I find that the majority of the seeds of a cross are germinating, I take that bag out and leave it at room temp until the root grows and a little green leaf appears. I then plant the little seedling in seed starting mix in a plastic drink cup with holes punched in the bottom. I put around four to six seedlings per cup. This process of damp chilling is stratification. I leave the seeds in the fridge stratifying for a month, unless they have been removed because they germinated early. As I mentioned earlier, I check about once a week and remove any bags where the majority have germinated.
I started stratifying my seeds in mid October and have some seedlings growing that were potted up on November 23rd. These have been growing under lights and are quite large now. I stratified groups of seeds every few weeks up until the end of January. I find it easier to do this way, then they don't all have to be potted at once. My light stand has three shelves, so I can adjust the height of the fluorescents to accommodate the different sized seedlings.
I do lose the odd group of seeds to rot, but I just think tbose seeds weren't viable.
This method seems to work for me. I am sure there are lots of different methods that people use effectively. It is a matter of trial and error to see what suits you best.