Kind of figured out most of what I needed. Just needed to read a little. Not sure if I can delete this thread.
Let's keep the thread. Maybe someone can find it useful at some point.
Hard to gauge the amount of yeast you harvested.
Is that a 1 liter jar about 1/3 filled with yeast (~330ml)?
Most (normal) yeast growths 4-5 times the pitched amount, depending on viability, age, gravity of wort, etc.
To answer your question, yeast can last at least a year in the fridge, even longer. Count on losing 5-10% viability (healthy live cells) per month. There's little need to "wash" it, a little trub and dead cell mass won't harm your next batch, unless it has autolyzed badly (died and disintegrated) and smells terrible (burnt rubber, liver, death).
When "washing" yeast you easily stand to lose 50% of live cells suspended in the trub layer, that you'd toss out. In most cases you can pitch the somewhat trubby yeast or make a starter with it, especially if it isn't too old.
It's really yeast "rinsing," as washing would incorporate the use of some sort of acid to kill or at least reduce bacteria.