For sure it is better to let them sit longer - viability is best when seeds are ripe, riper, ripest and even dry when pulled from the plant.
I wouldn't cut a seed head and expect it to finish ripening indoors. Everything I read says to let seeds stay on the plant until they fall off. But maybe you can!
I hope VA doesn't have drizzle-every-day while you're trying to collect seeds. I have Fall drizzle, and it makes it impossible to get seeds from late zinnias or marigolds. I can collect any number of seed heads pretending to be wet, moldy sponges!
If you're concerned about losing seeds when they drop off, maybe use paper bags on days it is not raining. Or just hope that spinach retains its seeds as one site hinted. When they say "haul the dry, brown seed stalks indoors and THRESH them", I figure that the plant will hold onto enough seeds to let you collect a lot.
P.S. I think the easiest way to clean seeds is to collect 2-3 times as many as you need. Then save only the ones that fall out with minimal threshing. By creating almost no chaff, you hardly need any cleaning.
Then save bags of the leftover seed+chaff without ever getting it very clean. You can plant those yourself. Or re-clean them if you eve run out of the first, cleanest batch you collected.
By the way: congratulations on preserving our Spinach Independence from corporations that may not share our values!
Maybe you can find or found a local seed library.
http://www.seedlibrarian.com/
Oops. Territorial says that Olympia is an F1 hybrid. Some F1 hybrids produce F2 seed that is pretty close to the F1 crop you grew. Others have a lot of hybrid variation even in the first year (F2 crop).
Probably seed saved from the F2 crop you and your friends will grow next year is likely to produce a quite varied F3 crop. Roguing out undesirable plants and saving seed only from the best and slowest-bolting plants will tend to select for the traits you want, but really saving seeds from OP varieties will reward your efforts better by giving you an optimum crop every year with much less need to rogue out poor plants and search long and hard for ideal plants to allow to bolt and pollinate each other.
http://garden.org/ideas/view/R...
