I found a part of really old episode of Inazuman on Youtube and tried to find out more about that series.
Somehow I think it was not the Grand Championship cars which inspired the bosozoku, but rather this series with this weird flying car called Raijingo!
On Youtube I found the hilarious opening of the series:
WTF? He is able to rebuild collapsed buildings and shoot ropes, like spiderman, and pulls the building erect again?
According to the reviews of the series I found out that the flying car called Raijingo actually has a psychic link with Inazuman. Raijingo is capable of shooting missiles from its mouth. The car looks like it was originally a Nissan Fairlady 1500 SP310. Raiji means thundergod in Japanese, so it would have been more logical if the car was based upon a TE27 Trueno!
This was the part of the video I found and be prepared for a thrilling car chase between Raijingo and a Nissan Gloria A30: