Anybody have tips on how to get to this level of solder-fu?
Really, learning how to braze and weld steel helped me a lot. Heat control is extremely important. Heat flows, and you learn how to position your iron to get the heat where you need it. You can also tell how hot something is by how the puddle looks.
Then practice with PVC insulated wire. The PVC insulation shrinks if it gets hot so this is good practice at speeding up.
I looked through the NASA document and most of it is not advance technique.
EDIT: people are saying "good tools" and I wanted to say a bit more about that. You can buy an iron for a few dollars from ebay. Don't use those. But almost any iron above that is going to be fine. I'd prefer to always be using Weller or Hako, but failing that any of the chinese no-name irons with temperature control are going to be good enough for most hobbyist projects. I love my Lindstrom and Bahco snips, but you can get good-enough cutters much cheaper. If this is something you're going to be doing all day every day you'll want to invest in the tools.
If you're looking for a practical way to do this, consider hand-wiring your own keyboard. I did this a couple years back, with 75 keys or so. With the diodes on each key, it was about 225 solder joints plus whatever extra to land the matrix leads on the microcontroller.
Good variety, too. Some were wire-to-wire joints, others were wire wrapped around post, and a few where through-hole joints.
If I look at the underside of that keyboard, I can tell where I started and where I finished by how clean the solder joints look :)