I would give them advice.
1. Stay home and fix your own problems ...create a country that you don't want to leave.
2. The entire world can't live in America and Europe. See #1...
They have already left their countries..... So....
You would give them a boat to go home with and educate them to overthrow their governments?
If there are caught here illegally they would never have a chance at citizenship. We would have prisons made up for Illegal's who are caught. It would be hard time, not club Fed or the free vacation modern prison is. They would be doing hard labor and or making products to sell to help cover the costs of running the prison. Also all prison documents and signage would be printed in English only and no translators, they can use another prisoner for that. Some motivation to learn English. We don't adapt to them, they adapt to us.
The wall would be completed, there would be more Border Patrol and Ice Agents, more CCTV on the fence, drones flying 24/7 patrolling our border and equipped with GRP to locate the tunnels. Also the Coast Guard would get a boost in people in equipment to protect the waterways from Illegal's and Narco Subs. They would get drones as well.
If the penalty is harsh, it is more of a deterrent.
I agree with about 96.4% of your proposal. The monkey wrenches are the private prison system on the stock exchange revolving doors and the cost/value to the wall/land border, and the in effect blockade.
The coastguard/ICE/border control collaborative would easily outscale our Navy + we'd have to create another coast guard to take on their own ridiculously gigantic mission. Those guys and girls are heros anyway you cut it. Anyway, the last monkey wrench is the 'American Gangster' reality. Americans buy tons of drugs that can't be sourced in the U.S. period. They get through pretty often. The 'war on drugs' doesn't cross our southern border it's a war on Americans on American soil.
Add to that the drugs that are being made in Amethica are also being made in Methsico and South Amethica in mass quantities. America imports their variety of products, and we shell out big bucks for them. There's private airplanes that have been operating import markets for decades. Frank Lucas was real George Jung was real and they weren't the source, they were logitsticians, middlemen. There are hundreds if not thousands of them now. It is undoubtedly unfortunately a business, and it has grown and diversified to meet various demands.
As for the wall in particular, even if a great wall of America was built it wouldn't deter chaote from becoming mariners and charging more for their 'services'. Anyone who has been out on the open ocean where you can't see land in any direction can tell you that you can't catch everything. There's entirely too much water and too much coastline. Any parachute deployed over the U.S. would have to be tracked as well and if the number of drone incidents near airports in restricted airspace are any indication this is quite literally mission impossible. . .
We'd need China's population dedicated to the line of defense. Isaac's analogy is very fitting for immigrants, not actual refugees. I'll take Conrad's numbers on the Chinese but that point is the same. Revocation of the anchor baby policy is an absolute must especially for Chinese who are limited to how many children they are allowed to have there. India's middle and upper castes who can afford to send their children abroad to study medicine and law. Also the sanctuary cities have to relinquish that --stupidity--, no other way to say it.
The key to immigration reform in the U.S. in particular regardless of their rap sheet is not putting them in American jails and prisons or detention centers.

yes. Here's why.
Prisons, state, Federal, and private (worst offenders) have limitations and quotas. One cancels the other unless we build more prisons (tax payers and locals notice things like this sometimes). The prisons work somewhat like isaac's analogy. The quota and the capacity dictate the stay more than the crime dictates the sentence. The most profitable prisoner is the short stay, not an actual lifer. A criminal on the street ensures police job security and court fines fees legal fees tickets... The way to hide prisons from citizens is to make thempprivate. Their stock varies depending on their capacity, capacity drops with growth (new prisons) and law enforcement and court quotas rise based on the available positions. This works great for the private companies like CCA, and police forces that need or are able to grow, but their capacity is limited by their jurisdiction. Nypd will not spill over into Pennsylvania or Maine. CCA however is able to funnel returns where population growth is high, crime rate is high, or where the stateor city jails and prisons are overrun aging or not profitable enough to warrant new state funded prisons. Illegal immigrants factor into this heavily, bolstering low quotas alleviating cap room or bursting capacity where a new prison is wanted. One entity actually stands to profit from this, the private stock traded prison companies.
Sanctuary cities serve as 'loading docks', citizens unemployment goes up, crime rates increase and when immigrants have scraped up enough under the table they move somewhere nicer and send their anchors to school. All that said they do some jobs that are difficult or nasty but Americans have become a bit less picky about their jobs because cost of living is through the roof.
Catch them, no i.d., no VISA, no passport, no greencard, put them on bus to Tijuana. Period. No exceptions. No incubation period, if they have criminal records hand them off to Mexican prisons. Repurpose Guantanamo, let them eat tortillas. To hell with a wall that makes it harder to find their entry points, leave a 2' 6' door open 24/7 with attack dogs and armed guards and start shooting down private planes that don't answer the towers with pre planned flight plans and manifestos. Anything drug person found by customs results in immediate permanent revocation of citizenship and exile for Americans and death penalty for non Americans.
Cruel sounding, I know. But it WOULD work combined with strengthening our navy's cruisers enough to put fear in the hearts of smugglers and chaotes.
^ For illegal immigrants chaotes and smugglers, not expatriates who enter legally documented on temporary Visa or refugees.