Look at the picture I just posted. It uses the insight body shell, just with a serious, serious roll cage. It's not dropped over anything. The insight engine bay is big enough, with some modification, to fit the K24. The front clip is all still Insight body in white.
Before that they had a K20 in it, which dimensionally is almost identical to the K24. Here is an article talking about that:
http://www.hondatuningmagazine.com/events/htup_0903_bonneville_speed_week_fastest_honda/