I thought a lot about it, and I think I found a simple solution:

Keep the current h1b caps, and then auction off each visa to the highest bidder. The auction proceeds must go to the employee in question, with jail term for anyone trying to claw it back.

What this will do is drive the wages for the immigrant engineers ever higher, by extension raising the wages of Americans as well. It will also make sure only the best ones can be brought in, stopping the "cheap import" problem, and the higher wage will give the best incentive to come. Resultingly, foreign companies will be drained of talent, and American companies will become even stronger against weaker adversaries, and employing much of the best talent in the world.