I store dry seed in the refrigerator, the 'butter keeper' tray keeps them from getting lost in among the food. Dry storage in the refrigerator extends shelf life over just sitting in a desk drawer. Seeds of 2 needle pines, such as Japanese Black pine, Scotts pine, Jack pine, Pitch pine all have shelf lives of 5 to 10 years and still retain better than 50% germination. Seeds of some white pines the germination rate drops rapidly, at one year germination rate can drop to only 50%. Japanese White pine and Chinese lace bark pines are examples of this. Shelf life of dry seed is fairly species specific, though you can make generalizations for certain groups. I believe the elm seeds will be good dry for at least a couple or more years.
Dry storage in a refrigerator does not count as stratification, stratification only happens when the seed is moist and cold. Wet paper towel, or moist sphagnum moss, or moist perlite in a plastic bag can work to stratify seed, or one can plant flats in autumn and then leave the flats outside for the winter, the seed will sprout in spring if the plant is hardy in your climate zone.
Maples in general have an interesting issue, if seed is sown while still fresh and moist, in autumn, it will sprout in spring. Seed that has dried out will require both a warm stratification followed by a cold stratification. For Japanese maple I would plant seed in early summer, keep the flat moist, leave the flat out for the winter, to have the seedlings sprout in the following spring. Maples have a "mixed" behaviour, a small percentage of seed will sprout right away, then majority will sprout 'on time' according to the treatment. Japanese white pine also shows this behavior.
Most 2 needle pines don't need any stratification, can be sown in spring, but better more uniform germination will occur with a stratification period.
It is best to hit the books for each species as seed germination requirements can vary widely. The better seed companies provide the information needed. My current favorite seed company is Sheffield Seed.
https://sheffields.com/SEEDS