You already kind of can. While in a replay, pressing the screenshot key should open a popup similar to the render settings, if you then choose the Cubic option, it'll render a single image consisting of the 6 images you're looking for. You can then just use your favorite image editor to split it into whatever format Minecraft requires.
I don't think adding a special option to output directly to MC's format is worth it since it's essentially just MC's Main Menu format, no one else is using it.
