However, if we issued an appropriate number of visas, then we would cover domestic needs and Mexicans would no longer have an incentive to jump the border. We could do that by selling visas at market rates to eligible Mexicans and other Central Americans and monitoring the prices of visas and field wages to get the number more or less right.The system does not have to be perfect. As long as Central Americans can buy visas at will and U.S. employers can obtain low-end labor on demand—even if it may be a bit costly at some times—both Mexicans and the U.S. businesses sectors would have an incentive to use the system.
Call them "Opportunity Visas" because that is what they are. The idea that the Mexican or Central American person can buy a chance to make 4 times more than their home country would be very enticing. The article says Visa jumpers would be deported and then ineligible to buy another would be a strong disincentive to try to sneak away. Then you would have to apply a strong stick against employers hiring foreign nationals that have not purchased an OV. Huge fines or even jail time for employers would prevent them from skirting the system.
A big thing to nail down is the the term that an OV lasts for. Maybe allow it to be active for 3 years and then the person cannot buy another one for a year. That would prevent someone from staying in the country indefinitely. Maybe allow the employer apply for a re-new depending on the worker. That way they won't lose a trained foreman or something due to the OV running out. You would need to figure out if the OV-holder has a kid during the employment period who would automatically be an American citizen. I would consider having the kid leave with the parent when the OV runs out. After the year off period the OV-holder can then bring the kid back into the country very easily afterward.
The other thing they would need to figure out is the price of the OV. I would suggest making it based on the job applied for. That way it could work for H-1B visas as well. So a computer programmer would cost several thousand but a fruit picker would be a few hundred dollars. You may even allow the employer to pick up some of that tab. If you need more fruit pickers or programmers then the company will need to subsidize bringing them in. You might also see the Mexican government paying for OVs which would be fine as long as there is a job for the person. You would need to figure out what would happen if the OV holder loses their job. If it was for cause then they have to go back. If they are downsized then they need to return to their homes and reapply for something new but their OV is still good in the meantime.
Finally, you need to add a layer of tech to the process. Make the OVs have chips in them and require the employer to scan them periodically for auditing purposes. Then you can get an accurate count of who is in the country and doing what job and how long they have left on their OV. Maybe you could have the card be eligible to purchase health-care and be used as identification to open a bank account and other financial transactions. They might even have a link to the employers account so they can pay them on the card and have the OV be used to purchase things. This would prevent a cash-based underground economy from continuing to flourish. Of course you would need to prevent counterfeiting and spoofing and such but that would be required anyway.