I cannot tell if this is willfully pedantic or not. And well, since we are being pedantic, I guess I will allow myself to say, that you can't re-license per se, only newer versions can be re-licensed. a prior release will forever be that license.
Now, with that said, modifications made to a GPL codebase, when published must be under the GPL. This is where the virality or copyleft come in. This in turn means that a GPL codebase cannot be anything but GPL. Putting BSD licensed code inside a GPL codebase is like pouring fresh water into the ocean. And even if you did do that, it should be a separate codebase, because if its a direct modification, then that should be GPL as well.
Now, with that said, modifications made to a GPL codebase, when published must be under the GPL. This is where the virality or copyleft come in. This in turn means that a GPL codebase cannot be anything but GPL. Putting BSD licensed code inside a GPL codebase is like pouring fresh water into the ocean. And even if you did do that, it should be a separate codebase, because if its a direct modification, then that should be GPL as well.