The one game that really comes to mind is BADLANDS by Atari (1989):https://en.wikipedia.org/wiki/Badlands_(video_game
The course needs to be a lot bigger and the screen needs to follow the player around, but Badlands has a nice setting and feel to it.
This genre really needs an upgrade, and I think so much could be done to it in terms of movement and weapons. Maybe even have some kind of driving/flying/boating crossover, like at a certain point the car will transform to about across a pond, fly over a canyon, etc.... And you need to hit specific targets for that to happen.
I also think twin stick-controls could be used, and maybe even controlling both yourself (left stick) and a drone (right stick) at some point.
Finally, I think you could have so much fun making this!