In the end, the only thing that matters is that you like it. Well, the main thing is that you ride it. Ride it until it won't ride no more. Not worthy of any upgrades in my opinion. But again, that is for you to decide. You mention going with lighter components, stem, bars, etc. I wouldn't bother personally. What are you going to accomplish? If you are doing it for weight reduction, as you already said, at 350 lbs. what's the point? If for enhancing the attractiveness or general appeal of the bike, why bother?
Just accept her for what she is and ride the rubber off of her. That's my opinion.