I'm a little confused because I think you're using some terms differently than they're used elsewhere on this board. I think what you're referring to as "crash cooling" is what the board generally calls "no chill." When most of us are talking about "crash cooling" we mean cooling the wort after fermentation to get everything we can to settle to the bottom before racking to keg or bottling bucket or secondary. Also, "yeast washing" refers to separating the yeast from the trub of an already used yeast cake to obtain samples of yeast to use in later batches. Maybe you're talking about doing that in addition to making a starter? I just want to make sure we're all on the same page so if you have a question later we can spot what you're talking about right away.
To answer your later questions though, I do exactly what you're proposing here. After the boil the first thing I do is collect starter wort from the kettle. Regular glass will likely break. You can use Pyrex, stainless, aluminum, or HDPE plastic. My LHBS sold extract in 1/2 gallon milk jugs that were HDPE so I use that. Most ciders and apple juices that are sold in plastic containers are PETE and will melt at boiling temps. I eyeball about 1.5 quarts of starter wort and that has worked well for me. Just don't fill your container all the way up or you'll not have room to pitch the yeast into your starter. Also, I don't use an airlock. I just sanitize some foil and put it on top.
Next I pour the rest of my wort into the Ale Pail and seal it up. When the wort cools, it's going to contract the air in your fermenter a LOT. It'll suck a regular airlock dry. I used to use a long blowoff tube and a sanitized jug of water for the airlock. When the air contracts, it'll suck some water up the blowoff tube but not enough to suck water into the bucket. These days I just dip a cotton ball in some vodka (it was tequila last time since I was out of vodka
), jam it in the airlock passage, and call it a day.
When the starter gets going, I pitch it into my Ale Pail and shake the snot out of it to aerate the wort.
Now let's talk about time. Any time of year, your starter wort will cool overnight (or sooner if you actively chill it). In the winter, your fermenter full of wort will chill overnight outside. In the summer (or anytime your overnight lows are in the same ballpark as room temperature), it will take at least a full 24 hours for your fermenter to get to pitching temp. Also even with a stir plate and active cooling of the starter wort, you're probably not going to have a starter ready by the next day by morning or even lunchtime. It takes me overnight to cool the starter wort and a full 24-48 hours from the time I pitch yeast into the starter until I get the starter going well enough to pitch it into the fermenter. I'm not saying you can't get a decent starter going in your timeframe (especially with a stir plate, chilling your starter wort, and a really fresh yeast with fast-fermenting characteristics), but I would add at least a day to your estimates to be on the safe side.