In general to avoid IP legal problems in the USA you can't do all of that yourself. Generally one party has to do all of the reverse engineering and write a specification based on that. Then another party can take that specification and write a "clean room" implementation.

https://www.allaboutcircuits.com/news/how-compaqs-clone-comp...

Everything old is new again. https://en.wikipedia.org/wiki/DeCSS

It worked out pretty okay for DVD Jon but I imagine it was a little scary for his dad and brother at the time.

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.