I'm not a PE, but ended up with a CNSM degree after 2 years in ARE. Without doing the calcs, I'm trusting that you did them properly.
The downfall of your predicament is that no PE is going to assume liability without compensation. Even amongst friends, the liability is too high, and if their O&E insurer ever found out, it'd be akin to medical malpractice.
Your best bet is to find a local independent engineer, someone not working for a large firm, and get them to write the letter to the LAHJ for a couple hundred bucks at most. Consider it insurance just like your extra beam.