You are proposing a mechanism for determining the price but not the quantity. And, since the quantity can be arbitrary, then, thought bidding, so can the price

You are proposing a mechanism for determining the price but not the quantity. And, since the quantity can be arbitrary, then, thought bidding, so can the price (within limits). Furthermore, if the H1B is causing a cost/loss to someone, then the money should go to these people. You can argue that the H1B is harming local workers, but it cannot possibly be harming future/potential workers to which you propose to give the scholarship.