Is there a headspace, as well?

I still value freedom in what feels like a fundamental way, I just also value hierarchy and social order now.

Gygax would say your alignment has shifted a step toward Lawful. I tend to prefer the Exalted system, which could represent such a shift through the purchase of a third dot in the virtue of Temperance.

Given that you're abnormally intelligent, you probably need less information to deduce any given thing than most people would. The flip side of that is, other people need more information than you think they will, especially on subjects you've studied extensively (such as the inside of your own mind).

Given that you haven't figured out the problem yourself yet, they probably also need more information than you currently have. You might be able to save yourself some trouble (not all of it, but every little bit counts) on research and communication in step #3 by aiming step #1 at people who've already studied the general class of problem in depth. Does RIT have a psych department? Make friends with some of the students there and they'll probably give you a long list of bad guesses (each of which is a potential lead on the actual problem) for free.

Given that you're trans, you probably also have an unusually good idea of what you want. Part of the difficulty of step #2 is that other people cannot be counted on to be fully aware of, let alone adequately explain, their own desires.

If your introspection is chewing itself bloody, maybe it just needs a metaphorical bite block. Does RIT have a group of people who get together for tabletop roleplaying games? Those are going to be big soon. http://thealexandrian.net/wordpress/24656/

The goal is to connect with people who will, for one reason or another, help you without being asked, such that the help will keep coming even while you are unable to ask. They don't necessarily need to do it consciously, or in a way that makes any sense.

What exactly do you mean by "writing?"

The "superintelligent tool" in the example you provided gave a blatantly incorrect answer by it's own metric. If it counts suicide as a win, why did it say the disease would not be gotten rid of?

If all it took was "a little common sense" to do interrogations safely and ethically, the Stanford Prison Experiment wouldn't have turned out the way it did. These are not simple problems!

When a medical expert system spits out a novel plan for cancer treatment, do you think that plan would be less trustworthy, or receive less scrutiny at every stage, than one invented by human experts? If an initial trial results in some statistically significant number of rats erupting into clockwork horror and rampaging through the lab until cleansed by fire, or even just keeling over from seemingly-unrelated kidney failure, do you think the FDA would approve?

Google Maps has options for walking, public transit, and avoiding major highways; a hypothetical interrogation assistant would have equivalent options for degrees of legal or ethical restraint, including "How do I make sure Eddie only confesses to things he's actually done?" If Google Operations Assistant says that a few simple modifications to the factory can produce a volume of paperclips that outmasses the Earth, there will be follow-up questions about warehousing and buyers.

Reducing crime is comparatively straightforward: more cops per capita, fewer laws for them to enforce, enough economic opportunity to make sure people don't get desperate and stupid. The real problem is political, rather than technical, so any proposed solution will have a lot of hoops to jump through.

I suspect a crazy dictator with a super-capable tool AI would have unusually good counter-assassination plans, simplified by the reduced need for human advisors and managers of imperfect loyalty. Likewise, a medical expert system could provide gains to lifespan, particularly if it were backed up by the resources a paranoid megalomaniac in control of a small country would be willing to throw at a major threat.

I am now imagining an AI which manages to misinterpret some straightforward medical problem as "cure cancer of it's dependence on the host organism."

More specifically, fast forward to 2080, when any college kid with $200 to spend (in equivalent 2012 dollars) can purchase enough computing power

If computing power is that much cheaper, it will be because tremendous resources, including but certainly not limited to computing power, have been continuously devoted over the intervening decades to making it cheaper. There will be correspondingly fewer yet-undiscovered insights for a seed AI to exploit in the course of it's attempted takeoff.

Neglecting the cost of the probable implements of suicide, and damage to the rest of the body, doesn't seem like the sign of a well-optimized tool.