We don't disagree on that. We're probably talking about a chicken vs. egg problem, but I think that if these people have a choice between a legal and an illegal way to get here, the vast majority will choose legal.
We disagree where you said at #69 that we have no choice but to offer some form of legal status to illegals. We do indeed have a choice not to, and it's the right choice. If guest-worker status is made available only to people who apply in their home countries, that would greatly reduce the incentive to come here illegally. As you said, they'd have a choice between coming here legally and illegally, and coming here illegally would be the made the less palatable choice.
I don't believe that we do have a choice when it comes to the people who are already here illegally. The vast majority of them are working at jobs where they are needed, and they can't be replaced overnight.
The only way we can find out who they are and where they are is to make the employers report them. Employers won't do that if they risk their businesses by doing so.
I don't think there's any way even a giant bureaucracy can find many of them unless the employers cooperate.
I can see options like giving currently illegal workers a limit of something like 3 years, then making them go back to their home country to reapply. That would give both the workers and the employers time to plan for a change.
I think the goal should be to make sure that everyone who is here has some legal status, so we know who they are and where they are. Driving the illegals farther underground is a terrible option.