POST Ajax bad request

I tested your code and got it to work by removing the following line as it is unnessacary.

options.data = JSON.stringify(options.data);

You can also safely remove the following lines in your AJAX call.

contentType: 'application/json', // tried without it too
dataType: 'json', // tried without it too

Please check out AJAX in Plugins on the WordPress Codex for more info.