I don't quite see what's wrong with the fine concept. Fine them 2000 dollars. That's punishment for breaking the law and entering the country. What was preferred? A steeper fine? They have a job and they got caught and paid their fine. Then they have to endure the same wait for citizenship as any other applicant.
Why is this bad? Is a more severe punishment preferred? If you deport and fine nothing, that does not inflict any punishment for breaking the law. They just take all their savings with them. A fine does. Isn't this better than deportation? Do you want a higher fine? How much?
The job they hold is an ill-gotten gain that they received by breaking a federal law. Another amnesty will simply speed the rate of illegal immigration. Build the wall and deport. Simple solution, and the only one that will stop the problem.