How about we just keep the mazda badge? It is a mazda after all.
If one doesn't like the mazda logo or wants something a little different, there is Roadster badging... the car's a roadster so nothing wrong there. This whole trying to creat a history for a car with a badge thing is silly.
Mazda put their heads together and designed one hell of a sports car. They put everything they wanted in an open top sports car in one basket and created the Miata... Yes it took design cues from earlier cars from Lotus and MG and others, DUHHH - every single car that is produced draws upon and then builds upon the designs and ideas of cars that already exist. It's nothing special or out of the ordinary that when Mazda designers and engineers went about figuring out what they wanted for a lightweight two seater soft top car they drew ideas from many of the already existing cars in that class because those were cars that they themselves liked.
If you like the badge, cool. Use it. But the car is a Mazda. Not a Lotus, and that badge is an intentional immitation of the Lotus design and the car is not a Lotus so it has no place there IMO.
I think if somebody so badly needs a different badge for their Miata that they should design an original Mazda or Miata emblem for their car - be proud that it's a Mazda and of what Mazda created in the miata... don't shy away from it. And actually there are several original Mazda emblems out there already to choose from if that's your thing.