That's very similar to my own thinking, although I think your numbers for how quickly a million-ton mass evaporates are off. (The appendix to this paper
has decay times and power outputs.) Hawking radiation does make a lot more sense than fiddling around with accretion discs, especially since you're going to get that radiation whether you want it or not. Trek certainly has the gravity manipulation capability to alter a black hole's event horizon, especially inside a confined space.