After lunch, I showed him my progress so far, and he called his father. Turns out his father is a retired engineer who used to design the PCBs in Philips televisions. He agreed to look my designs over, so I sent my stuff over to him.
With his comments, I started all over and routed everything by hand. And this is how it turned out:
10 transistors less (because they'll never be used anyway). No more straight corners. Traces are 20mil wide, and have at least 20mil clearance to other traces. I'm pretty pleased with this -- and it got the OK from the expert as well!
On with the driver schematic and PCB!