The typical "clean room" process would be to have one group reverse-engineer the original and document it, then have another group of "un-tainted" people implement the spec.

This methodology has been shown to be an effective shield against copyright infringement, but it does not protect you from patent infringement. Presumably the spec is patent-encumbered specifically to prevent this type of "attack".

You also wouldn't have any rights to use any HDMI-related trademarks.