Short answer

Google Forms doesn't include a limit on the number of responses as built-in feature but you could extend the of Google Docs editors features though add-ons or Google Apps Script.

Alternatives

formLimiter

From: https://sites.google.com/a/newvisions.org/scripts_resources/add-ons/formlimiter

formLimiter automatically sets Google Forms to stop accepting responses after a maximum number of responses, at a specific date and time, or when a spreadsheet cell contains a specified value.

Great for time-bound assignments, event registrations with limited seats, or other first-come, first-served signup scenarios.

References

Extend Google Docs, Sheets, and Forms with Apps Script - Docs editors Help

Still don't have a solution for how to directly get values of unchecked checkboxes, but I was at least able to write a function that compares the correct answer to the submission.

This splits the correct answer into an array then compares each item to the submission:

function checkAnswer(answer, key) {
var kArray = key.split(', ');
var nArray = [];
for (i=0; i<kArray.length; i++) {
    if (answer.indexOf(kArray[i]) == -1) {
        nArray.push(kArray[i]);
    }
}
return nArray.join(", ");
}

Then I could call it every time I needed to report the boxes left unchecked. For example, with the doors question:

if (doors != correctDoors) {
  var doorsMessage = "Unlocked: " + checkAnswer(doors, correctDoors);
  report.push(doorsMessage);
}

At the end, I'll compile the report with:

report.join("\n"); 

And voila! The best I could do...

Ultimately, I'm still looking for how to directly get the unchecked boxes if anyone has a solution.