Establish work type categories and tie immigrant count to it. I think we already do this for some tech hard to hire categories. Expand it to include laborers, skilled construction, etc. Make it regional, urban vs rural, etc.
Require all illegals to register or face mandatory deportation. Give illegals who register a temporary work permit that must be renewed every 2 years.
Review the unemployment rate in these labor categories annually and allow/disallow additional worker visas and whether existing work permits can be renewed. Any workers with expired permits must self deport. Individuals failing to do so will be barred from future entry.
After 15 years of renewal approval for an individual allow them a 10 year or perhaps permanent work visa or green card.