Soldering the cells:
Heat shrunk & insulated the contacts
Charging the batteries:
Chair base sans-batteries
I forgot to take any pictures of it with the batteries inside and I didn't get any good pictures of it driving around (my phone crashes when I try to put it in video mode). Someone else took some video, hopefully I'll get that soon so I can post it. The chair now drives around very smoothly and has space for at least 4x the batteries I put in it for increased range. It still needs a good mount for the controls and possibly a better interface. Odds are it'll make an appearance next time miters has a booth for something.