You guys are making it too hard on yourselves.
No need to wash, no need to make a starter. After your beer is done fermenting, assuming it was a low-to-medium gravity beer (i.e., below 1.050), and you haven't added anything extra to the fermenter (i.e. fruit, wood chips, dry hops, etc.), just collect the entire yeast cake into 4 sanitized 1-pint Mason jars (I use the jars our pasta sauce comes in). After settling in the fridge for a few days, my jars are about 4/5 yeast, and only the top 1/5 is clear beer/water. Keep the lid cracked just an eighth of a turn, to let any excess CO2 vent out and avoid bottle bombs.
At the start of your next brew day, take one jar out of the fridge and let it gently warm up while you're brewing. When it comes time to pitch, decant the spent wort, swirl up the yeast, and pitch it. That's it.
No need for a starter. A starter really only has two purposes anyway - to verify the viability of the yeast and to build up the necessary cell count. As long as your yeast is less than 2 months old, its viability is fine. After all, by now you're likely drinking the beer it made for you, so you know they're hard workers.
As for building up a cell count, well, needless to say 1/4 of a yeast cake is more than enough cells to ferment another 5 gallon batch of beer, even if it's fairly high gravity.
You could go through the online calculators and determine its precise viability after the time that's passed, and it will tell you how much of the slurry to pitch, but you're still just guessing as to the cell density of what you've got there. I've had fantastic results just pitching the whole jar (1/4 of a yeast cake). It will take off very quickly and give you a great ferment. It's almost always a considerable overpitch, but overpitching is much less of an issue than underpitching, and commercial breweries pitch higher ratios of yeast than we do at the homebrew scale anyway. As I said, I've had fantastic results using this method.
Label your jars in the fridge with a strip of painters tape on the lid and a sharpie, so you can tell when a yeast is getting too old (I draw the line at 2 months) and discard it.
I would, however, keep beer styles in mind when doing this. For example, if I were brewing a nice, clean-tasting Kolsch, I wouldn't use yeast I'd harvested from a batch of particularly bitter IPA, or a roasty stout, as some of those flavours can carry over.
