Today I tried my home-grown OBD-ii interface in the car. At first it didn't work. I figured I probably had to boost the signals so I went back to the lab and made a solder bridge across the 200Ω resistor to maximize the strength of the active pull-down and added a 1kΩ resistor between the K line and Vbat for a stronger pull-up.
Now, when I send the byte 0x33 to the car at 5 baud it responds with three bytes 0x55 0x08 0x08 at 10k4 baud. This is the ISO9141 initialization sequence which means the circuit works!
I will probably try to weaken the pull-up/pull-down later but other than that the hardware implementation is pretty much done. Next is software.