Steering yoke.

It sounds like your best shot is to get a short, steep stem and put a bullhorn in it. Install the bar, as you said, with the tips pointing up a bit. You could try it upside down; that might actually work well. Whatever you settle on, get the right size frame for your body--don't mess with the main tube dimensions in an effort to bring the handlebar into a comfortable position.

Good luck, and please post pictures when you get it sorted out. Some of the guys here will laugh or make fun of your bike, but I'm curious to see what you settle on.