I believe I too easily mixed inertial and gravitational mass when looking through your initial maths, leading me to believe the F=ma stuffs were tacked on to give the desired result. Then I believe I might have had them not equal when I did mine. Or something. Thanks for the primer and the bolded beatdown ; I hadn't used that part of physics for a while, and it showed. I care to know the truth rather than that I'm right. Perhaps the Oh-My-God particles are being chased by negative protons.
I think I missed a step or two here. Last I heard there was NO way to change normal spacetime geometry to an Alcubierre bubble (although one would be stable if it for some reason already existed) nor to cross from the outside of one to the inside.
Well, at the very least, we're shrinking the required mass to make it work. That's a small step, and I'm happy with that.