How do /you/ minimize cheating (especially in math)?

[lglen]

Here what I've been doing, but my "Part 3" is not working... 

An "Exam" is in its own module (which I hate, but that seems to be the only way to do this). The previous module is a prerequisite and students must do the three tasks in the "Exam" module in order:

Task 1: An "Integrity Statement" - a one-question assessment (I use an external too) that lists the things they have to agree to, with radio buttons for "I agree" and "I don't agree". The "right" answer is "I agree". It's worth 1 point, but not counted toward the grade, and set so that the requirement for the "task" is that they earn 1 out of 1. If they try to bypass it or they click "I disagree" they get the "You haven't completed the prerequisite" message when they try to open the Exam. 

Task 2: the exam

Task 3: a single file-upload question that was supposed to help ensure that they were doing their own work. They didn't know which one question I was going to ask to see the work for until they'd completed the exam. The idea was that they would have to write out their work for all the questions, and only when they were finished would they know which question they were required to submit work for. I required that they do this within 2 minutes after the exam to ensure that they didn't just start then to write out the work for the question (in the admittedly likely rare event that a student had just looked up the answer online or used an app). But if I put a time limit on this, they can't do it in time, and if I don't, I have students who "need to rewrite their work" because it's "messy" or some such; I had one upload the work over 60 minutes after the exam, claiming his work was too messy and he had to rewrite it. For 60 minutes. For one question...

So...

...what do others do? I've heard all /kinds/ of advice from "use a lockdown browser" (which doesn't address the fact that apps on their phones will "show their work" for them) to "let 'em cheat!" 

I don't care if students don't memorize the quadratic formula. I let them use notes and I let them use their textbook. I've see some amazing learning take place /during/ an exam, even in a F2F class - that's another discussion, but I'd love to have it!

I just want them to /learn/, and that's not happening if they use an app to get the answer and "show the work"...