Agreed. IME yeast "washing" only tosses out 90% of the viable cells and doesn't improve viability much if any.
I wouldn't pitch onto the entire cake. If you don't have a microscope 1 billion cells per milliliter will give you a ball park estimate.
According to "The Practical Brewer" a six month storage cycle is common for yeast strains stored in a broth. For Agar slants it says over a year. Personally I've been counting cells on the ones in my fridge for over a month and seen no drop in viability. I just did a beer with a 6 week old slurry and it took off in about 24 hours.
Details on the effects of refrigeration on viability: