Apparently, by turning on mouse steering, I was able to control the car during the cutscene. It took a few tries, but I managed to get it to work. It's very picky about the specific angle the wheels are turned, however.
Also, another strange issue I found: Reimu doesn't seem to be gaining any muscle stat in the game. I spent a good 30 minutes lifting weights to date Millie, only to find the stat not move. When using the muscle cheat, the stat still didn't move. I ended up using the cheat with the CJ model, which properly altered the stat.