The best way to "reduce dependence on foreign oil," of course, is to use more oil.

If you merely reduce consumption, prices will fall, and higher cost producers (like America) will stop producing.  If prices fell far enough due to a drop in demand, the only country that would be able to produce oil cheaply enough to make a profit would be Saudi Arabia.

The less oil we consume, the more we will be relying on foreign countries to provide it.

Yes, but the foreign oil is increasingly made up of the heavy sour crude and your local stuff is much higher quality.

Your idea is interesting though. What would be more effective is if the local American producers did stop producing, but demand continued at it's usual pace, thus you would suck up the foreign oil leaving the american oil 'in the bank'.

It's a bit like a kid eating everyone else's sweets while he leaves his own in his pocket.

The only downside to this scenario is that the rest of the world would suffer very, very badly. But hey! That's never stopped america before!