Another possibility given corporate hunger for immigration (and massive pressure to keep the various H programs) is to auction of the H-1B visas.
After all, the claim is H-1Bs are needed not to lower wages but because they can’t find workers. So if money is not the problem, and desperation to find skilled people is, they should be glad to pay up.
Of course, the screeching over such a proposal would put to rest the story that it is not about saving money.
Prioritize student loans to American citizens for skills needed to fill H-1B jobs.