So, I actually got a small amount of soldering done last night and tonight. I got 2 more driver boards soldered up, one of which I tested a small amount. The one I tested seems to be working, for the most part so far. I verified that the chips are all able to communicate with the microcontroller, and that at least one of the LED output channels works for each chip.
Things went pretty smoothly overall with the soldering, mainly because I ordered and was using brand new 0.01" soldering tips. Two down and 4 more to go!
Very little progress has been made on the for-test 20-pixel box. I have 2 of the10 sides glued on. Things are gong fine with it, just very slowly. I hope to get it to the point where I can test the 3-color LED's relatively soon. I can pull the microcontroller out of the big LED wall to test with until I get another board soldered up.