But I agree that it isn't hard to find decent people already in the USA.
Furthermore I still like my suggestion of removing the H1B limit entirely. Make the importing company pay a substantial sponsorship fee for the H1B person to enter. And give the hired employee the right (which can't be signed away) to switch to another job as fast as they can land one.
You see, making companies swear that they can't find a qualified American just encourages them to lie. Make their incentive to be honest, and see what happens...
Cheers,
Ben