"And demand that extraction royalties be part of the bid process..."

There should be [and as far as I know always is] royalties paid for any oil extracted from federal park lands.
Of course, if you logging trees on federal park land there are royalties taken [actually for trees it's called stumpage].

As wiki says: "A royalty interest is the right to collect a stream of future royalty payments, often used in the oil industry and music industry to describe a percentage ownership of future production or revenues from a given leasehold, which may be divested from the original owner of the asset."
http://en.wikipedia.org/wiki/Royalties
And if it was a State park, the royalties would go to that particular State. I'm not sure about Alaska, because of their constitution, I would expect that even Federal land which have some portions of the royalties going to Alaska in addition to the Federal govt.

"We just need to hold on until there is no oil left in other places. (Like off the coast of Florida and California.)"

I have no doubt that a lot of people [including Senators and other govt officals] hold this view, but it doesn't make much economic sense. I think we should extract all this oil so soon as we can, because economically it makes the most sense. I do think it makes sense for a strategic oil reserve for military purposes. And if people really thought it was necessary I wouldn't be opposed to more types of things like the strategic oil reserve. But you can get carried away with this sort of thing and ANWAR is a bad location for this. And if you want "oil parks" let's study it, like we study a wilderness park.

First of all, we have a huge oil reserve currently in a good location, in the form of oil shale. We could probably keep 1/2 of this reserve for domestic and military use in case of an emergency. Lock 1/2 of this away until say 2050, and let the citizens of 2050 decide how they want to use it or keep it further into the future. Next, encourage the other half to be used- this will allow us to have the technology to effectively use the other 1/2 if the need arises. In addition, in federal ocean areas [in ocean shelf areas] find oil reserves, study them, claim them as reserve areas [which we intent to stop all parties from using].
So that basically the US has a say 10 year supply if tightly controlled use as in a national emergency.
And of course have a plan; such as whenever the need arises that the current strategic oil reserve needs to used, then a timetable of the other oil reserves is set in motion so that instead just 6 months you have 10 year supply.
I think trying to have much longer than 10 year supply is foolish, but we need to know more about these reserves, and in a sense the federal govt will need to pay money for such a reserve- in other have a oil company find oil, then pay them to cap it off. So it might a situation where oil company find and mine 90% of the oil and govt keeps 10% for future use [or it could end up being 1% or 20%].

One big problem with trying to hold a lot of oil in reserve in order to make money as compared to maintain security- is that there simply couldn't be enough oil to make enough money compared to the money we are losing because we aren't currently using them. In addition, the market demand for oil could reduce, due to future technology. It could like keeping a reserve whales for the purpose of selling whale oil at higher prices for lamp oil.
As just one example is the huge Methane Hydrate deposits in the oceans. Another is possible consequences to nanotechnology. And finally getting cheap energy from Space environment.