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Or perhaps I should say, I found an alternate solution?

What you're supposed to do at the Demolition Derby, according to the videos I have watched, is this:

However, I solved it in a different, unexpected way. While I was pushing the orange car towards the second ramp, the blue car (the one that always pushes you if you try to get anywhere near Mo) attacked and somehow got entangled and stuck with the orange car, touching at the same time the left edge of the ramp. While both cars where unable to move, I went around them and thew myself against Maureen's yellow car. This skipped a couple of the cinematics shown in the video but the explosion happened nonetheless and I could continue with the next stage. I doubt this was intended behavior, but in the end it got the job done.