Welcome to our site. I agree that you should be using a Ford power plant in a Cobra replica. There are a few out there with Chevys and they run fine but will be almost unsellable if it ever comes up. I come from a Chevy background myself having built and raced two Corvettes, a Nova, and a Vega (with a big block BTW).
Research some Ford engine options. The Cleveland is a fine engine but the aftermarket has kind of forgotten it these days in favor of the 302 and 351W. Of course nothing looks as good as an FE in a 427 Cobra.