Well, after digging through the CLD-99 service manual, and with some tips from this and other boards, I managed to revive things with these oh-so-sophisticated troubleshooting steps.
- Manipulated the one pulley I could reach with my pinky finger just a little bit. I believe this was Part 8 (motor pulley) in section 2.5 Loading Mechanism Section of the service manual.
- Manually worked the gear for the laser assembly back and forth a bit.
Believe it or not, that seems to have either freed something that was stuck, or (more likely) forced the computer to reset its positioning. I suspect that was probably what code E3 was all about - maybe things got stuck in a weird state when I powered it down last.
Now for the real fun of putting it through its paces to see if I knocked anything out of whack while taking it apart...