I realize you are trying to maximize the quality of education you are providing. I don't think you can use that as an argument against failing students who blatantly cheat.
There's not an easy solution, obviously. You are taking a risk when you do something that some other members of your faculty are not doing. You must realize, they are threatened by your attempt to prevent cheating, because it will become obvious very quickly when you find such high rates of cheating and deal with them appropriately, that they are not doing so. That will raise difficult questions, deans will notice. I think you might find, to your surprise, that there are many other people in the same position as you, but perhaps not as bold as you are. I would wager that that many, many other faculty members hate cheating as much as you, and are disgusted by the blatant plagiarism, but also like you are pressured by the current state of affairs to bury it.
I would encourage you to stick to your original guns, and keep grinding cheaters out of your class. First of all, your reputation will be established very quickly among students. Students who know they have to cheat will avoid you every semester, saddling other professors who are softer on cheating with worse students, and concentrating the best students into your classes. More to the point, students won't try to cheat in your class nearly as much once your reputation is established, so the amount of time you have to deal with it will, I suspect, go down dramatically.
Edit: This is way more congenial than how I actually feel. It's your responsibility, and every other faculty member's, to identify cheating and run those students out of the university. They are stealing from the students who are trying hard and mastering the material, by graduating uneducated and unprepared. When they go out and embarrass themselves, it reflects on every other student with that same university's name on their diploma.
As for the girl crying for 2 hours, who cares? Let her cheating ass go cry in her dorm, I think you have very weird priorities to let her waste your entire office hours (with honest students waiting) with her obvious, transparent attempt to manipulate you emotionally.