I really like your plan from the technological point of view, but I think that it has some flaws in the sociopolitical department.
Right off the bat, you propose buying a plantation, but those things are pretty expensive. Where will you get the money ?
The core of your plan is to develop, and maintain a monopoly on, technological superiority: in agriculture, construction, and warfare. Unfortunately, your technological advances must be incremental, by necessity -- you can't go from zero to digital computers, nor are you trying to do so. But this means that your technologies will be comprehensible to a well-educated Roman. This practically ensures that your competitive advantage will be stolen by your rivals very quickly. You avoid gunpowder for this very reason, but is it really that much harder to steal pulleys ?
You attempt to get around this with your death-watch guards, but who death-watches the death-watchers ? If I told one of your guards, "nine out of ten gods agree, you should allow me to sneak in one of my smiths to talk to one of your smiths, and BTW here's a purse containing MXXIV gold pieces with your name on it", what motivates the guard to refuse ? And what about all of your agricultural innovations -- will you watch every peasant ?
In addition, your timetable is too aggressive. You're proposing to move from horse-plows to powered flight in less than five years. But building an ultralight aircraft, or a fuel refinery, or even a Conastoga wagon, is a lot harder in reality than it looks on paper. Mere abstract knowledge is not enough; you also need raw resources, experience, and training. Merely training your smiths (who, according to the scenario's setup, lack your intelligence as well as your education) might take a couple years in and of itself.
I believe you also underestimate the social inertia involved. We have trouble with "skepticism, falsificationism, logic, mathematics" and birth control even today; what makes you think that you'll be any more successful in these endeavours in the pre-Enlightenment Rome ? That "I am the chosen of Vulcan" gambit can only get you so far, and might in fact backfire, because priests tend to take exception to their power structures being disrupted.
Right off the bat, you propose buying a plantation, but those things are pretty expensive. Where will you get the money ?
We were granted "enough money to live as a patrician for a year". I made an assumption about what that meant, since in those days all wealth beyond jewelry was in the form of real property (land) anyhow. Agriculturally Spain was traditionally relatively crappy. Land would be cheap and plentiful because it wouldn't be seen as a viable resource for crop harvesting. (I'd only be able to pull it off because of modern agricultura...
A recent discussion post has compared the difficulty of an AI destroying modern human civilization to that of a modern human taking over the Roman Empire, with the implication that it is impossible.
The analogy has a few problems: first, modern humans don't have much greater raw intelligence than the Romans, only a bit more knowledge and tools; an AI would have a genuine intelligence advantage. Second, a high-tech civilization like ours offers many more ways for a genius to cause chaos than existed in classical Rome: it's more plausible that you can throw a few existing technologies together to create a superweapon than that Ptolemy could have done likewise, and there's no ancient Roman equivalent to hacking a nuclear launch system.
But taking over ancient Rome might serve as an interesting upper bound on the difficulty of an AI taking over modern civilization. And it's a theme of Harry Potter and the Methods of Rationality that rationalists should be able to come up with creative solutions to seemingly hard problems. So if Professor Quirrell offered it as an extra credit assignment, how would you take over Rome?
Here are the rules:
- You are thrown back in time to the year 1 AD. You can choose to arrive anywhere in the world, but your method of arrival cannot itself give an advantage (you can't appear in a flash of light in the middle of a religious ritual or anything).
- You do not start with Roman citizenship or any other legal record of your existence.
- You keep your original physical characteristics, including sex, height, and fitness. You will appear in period-appropriate dress of your choosing, and can't carry any artifacts with you. You may start with enough money to live a patrician lifestyle for a year.
- You are intellectually near-perfect. You know all human knowledge as of 2012. You speak fluent Latin (and all other languages of the day) and can orate as eloquently as Cicero or Demosthenes. You are a tactical genius of the order of Caesar and Napoleon. And you have infinite willpower and goal-directedness: aside from human necessities like sleep or food, you need never rest.
- You win if you either become Roman Emperor (and are acknowledged as such by most Romans), or if a state you control conquers the city of Rome. You lose if you die, of old age or otherwise, before completing either goal.