I think a very high application fee is actually part of a good solution, but is useless by itself.
A flawed proposal:
* Dispense with the 'need to search for a qualified American' which just complicates the process without achieving the stated goal, and includes a ton of legal and bureaucratic expense and time.
* A large application fee paid from the company to the federal government.
* The worker's relocation expenses must also be covered by the company.
* The worker gets a 10 year work authorization on the day of their arrival.
* The worker gets to leave their sponsoring employer on the day of their arrival, if they choose to. The employment contract may not include any clawbacks of anything.
The latter bullet is the key one. That's the one that uses market forces to truly enforces this person is being paid above market wages, and is being treated well, at their sponsoring employer. (which in turn means they don't undercut existing labor in the market).
It also means that employers don't really look abroad unless there really is a shortage of existing labor. But when there is a true shortage and you're willing to spend, the door is open to act quickly.
The obvious defect is that it creates an incentive for the employee to pay the federal fee themselves (hidden) plus more for the privilege of getting sponsored, and the company basically being a front for this process. Effectively buying a work authorization for themselves. I'm not sure how to overcome that. Then again, the current system could also suffer that defect (I don't know how common it is).