I finally got my order to go through. The trick that helped me: if you get to the final screen and your purchase times out, click back to payment details (the prior screen) and try again from that step (instead of refreshing and starting over completely). My purchase went through on the second try after backing up this way rather than starting over again. I hope this helps someone snag their order!
Mine packed overnight as well (sometime after 10pm), after ordering about 24 minutes after launch. No shipping details yet. 512 model. Props to Valve for moving things along pretty darn fast!