I’ve been “chaining” my starters for a year to get multiple batches out of one pack. Basically I create/step-up the starter I need for a given batch. Let it ferment out, cold crash, decant on brew day. During the boil I boil up another batch of starter wort with DME and cool it. Then I pitch most of it into my beer, saving a bit to pitch into the now-cooled starter wort. That starter ferments out over time and goes in fridge for later use. I do my starters in flasks, and use sanitized foil and a rubberband in the fridge for storage.
What do you think? Washing seems like more work and most yeast washers recomend that you create a starter from the washed yeast anyway.