Authentic Engagement with Mistakes

One question I've been grappling with a lot this year is trying to help students authentically engage with their own mistakes and misconceptions. My first year of teaching I was the queen of corrections, letting students correct every test and quiz to try to realize what they did wrong and learn from it. My middle schoolers were generally very honest about this, but when I switched to high school I saw the huge desire for good grades outweigh the desire to learn from errors. I saw more and more cheating and less and less studying for the initial test and I cut it off. 

I know there are such huge payoffs for kids who learn to analyze their own mistakes, though!! And telling a student who genuinely wants to learn from what they did wrong and is proud to demonstrate to you that they've mastered a concept that they are out of luck? It makes my stomach turn! 

This is very much a first draft, but here's what I'm thinking....

Things I'm considering:

• Only allowing students to re-test on a set number of assessments per semester (2....3....suggestions?). This allows the opportunity to make up for a "bad day" but not get used to failing the first time and making it up the 2nd time around. Does this go against the whole idea of always being able to learn from their mistakes? 
• I only want to offer 1 re-test....what if a student in genuinely absent? Do you start making exceptions?
• About 1,000 things I haven't even thought to worry about yet

Has anyone come up with a system they really love for allowing students to learn from their mistakes and prove mastery without sacrificing the high expectations on the first assessment?