i garden strictly in pots in the apt/balcony and store them in pots too.
I have huge 'Red Flash' - grown strictly indoors. and med to smalls 'White queen', 'FL sweetheart' and 'Miss Muffet' for balcony.
usually i wait until all the leaves decline.
when i see leaves dying off one by one (usually in sep-oct-nov depending on variety) i water just a bit. when the last leaf is left - no more watering until spring. i stack the pots and put them in plastic bags, tied up top, so i won't overturn them and spill the lot and stash them under the low table where it's darker and cooler near the northern window/balcony door with some draft. so it gets about 58-60F there at night. and that's it until april.
then i lift them and inspect and clean them off with a brush and remove the dried skin on the bottom. at this point if there is rot - it' s usually a goner. although i tried a few times to scrape them clean, dust with cinnamon - but it isn't worth the bother, unless the tuber is large. but it's the smallest ones that rot easier, of course. I don't loose large tubers at all - that is if they are at least an inch in diameter. the very small dwarf varieties like Miss Muffet have very small corms - half an inch at most. those i loose a few at a time.
but i never wash them and never dry them. after they are brushed, if i am not ready to start them, i pack them in very barely damp LF sphag, covering tops too and put them in tomato clam shells that have perforations on the side - to breath. even if they are showing the signs of life, they can still hold like that for another month or even two (sometime i dig them up earlier..like beginning of march...so they have to stay put another 6 weeks).
IF i want to start them, i dampen the sphag more and still close the clam-shells, but put them in the sunny spot to warm them up and then check on them and re-moisten them weekly.
when the roots are 1 inch - i plant them in pots. i noticed that when i start too early they take 4-6 weeks to grow roots, while when it's mid april - it'll be 2-3 weeks only. so i don't bother starting them early anymore. so in may they shoot up indoors on a western window and that's where i keep them until june or end-of-may at least.
i used to dig them up for inspection in the fall - but they dry up more, when dug up . so storing in dried pots is much better and less work for me.
i took up this funny pic of one of my large tubers of 'Red Flash' ready to go in the pot (have it for about 8-9 years?).
i used to dig up 'Red Flash' and store them dry naked in perforated tomato clam-shells. that worked too. but not for small corm varieties - too many would dry up.