That's great you know what elasticity is, but you still don't seem to get a couple of things: one is that demand curves do at times have inflections, and the other is the time scale of "long" term demand response in the oil market.
On inflection points, what they don't teach in Econ 101 is how price gets set. One learns that supply and demand forces determine it, but which one is predominant? The simple version: In a market without constrained supply, as in a market with some excess supply capacity (like the oil market pre-2000), price is set by the cost of supply. It will roughly equilibriate at the cost of supply plus marginal profit.
In a constrained supply market, OTOH, price is determined by demand, whatever people are willing to pay for the available supply, which is often much higher than the cost of supply + marginal profit.
Say you have 12 artisans who can each make 12 widget per cycle, and it costs them $1 to make each widget. If you have 10 buyers, supply is unconstrained. 10 artisans will each make a widget, and they will sell them for $1 plus a small margin. The other two artisans will simply stay out of the market. It doesn't matter how much the buyers are willing to pay, because the sellers are competing against each other.
Change that scenario, and now you have 8 new widget buyers walk in the room, so now there are 20 buyers and still 12 artisans. All of a sudden, there aren't enough widgets to go around. Now the buyers are competing with each other, and the price they pay will be just greater than whatever the 13th most eager buyer is maximally willing to pay.
That is essentially the situation we saw early this century. Rising third world demand flipped the oil market from a buyers to a sellers market, and price spiked very rapidly. The demand response curve went through an inflection point, where it basically didn't respond to price. But the points are:
a) that is expected behavior in this model
b) and that demand won't continue to be non-responsive to price change.
And in fact, in real world data we see this right now. Past $3.50/gal and onto $4.50, we're seeing significant demand destruction. Consumption has been dropping appreciably over the last year, and price is now even dropping. That alone makes it pretty tough to argue that price is actually that inelastic in the short term, or that high price actually increases the inelasticity. It's the opposite in fact. both short and long term.
On what a the "long term" is related to oil market elasticity: your estimate of "decades" is too high. Roughly 2/3rds of oil is used in transportation, so lets look there. That's passenger vehicles and shipping. What are the time scales for shipping contracts, retail supply contracts, vehicle product cycles and individual people's lifestyle changes in response to high transport costs?
It isn't weeks, but it also isn't decades. More like months to single digit years. There's no exact value, but we could say 5+ years is a sufficient response time to be considered long term, and 10 is certainly enough. I believe that's roughly the range economists use in their models.
Which brings me to another point: The economists who came up with the 1%/3% estimate have access to all this information and much more. You or I could make our amateur guesses about what response will be and how long it takes, but neither of us is really qualified for those guesses to be credible, especially to override non-amateur estimates.
I don't necessarily disagree with you though that drilling may be the smart thing to do in some cases. It probably won't put trillions into our pockets, because it isn't just a pile of money sitting there easily accessible. To pull out trillions of oil probably will cost trillions of dollars. In any endeavor, profit is revenue minus total cost, which can't be ignored. But certainly, it would be many billions in profit (maybe even a trillion or two... I don't really know what the margin would on OCS oil drilling in the future) in the form of revenue for government (if we smartly charge a sufficient amount for them, like you suggest) and increased economic activity. That may very well be worth whatever the environmental and aesthetic risks are.
Also, global warming is a concern. I agree with that too. I wouldn't recommend subsidizing wind farms though, since what we need specifically are fewer fossil fuels burnt rather than more wind power. We should just cap and trade carbon emissions and let the market decide how to respond, but that's a discussion for another day...