Just a rough start but...
1) End the drug war, increase economic and security aid to Mexico/Central America, and use diplomatic help and pressure to get local governments to stabilize their situations. Stamp out the cartels once we've made them broke.
2) Institute a broad vetted guest worker program for Mexicans/Central Americans/Haitians. All participants will be entitled to full US legal and labor protections as well as pay taxes at applicable rates. People from this pool who marry Americans should be able to access expedited permanent residency and eventually citizenship.
3) One time blanket amnesty for everybody already here and who can prove they've resided for x number of years (open to debate on the number). There is simply no other way to resolve the existence of a huge underclass without bringing everybody into the system. DACA eligible persons can apply for citizenship. Adult arrivals get non-revokable permanent residency with all commensurate legal protections.
4) Mandatory employment eligibility screening. If people/companies try to circumvent or employ illegally then they go to jail, not pay fines. Especially for corporate officers who are looking the other way.
5) Entirely restructure the US visa system to prevent overstays and track people who come.
For 2, why allow people to be expedited because of the country they come from?
How do you do 3? If you announce a date, you are going to get a flood of people coming over. If its a window to register, how do people prove they were here and did not come in after the announcement?
How do you support your argument for 4? People drop out of work regularly. Are you going to deport someone because a business shut down? What sort of window are you thinking?
5 while doable is going to be very expensive. Not sure what you mean as a solution here.