Convert HTML input string to JavaScript Array literal
The answer

What you're actually trying to do is only converting objects from Javascript notation to actual javascript objects. Now what if there was a well-specified data interchange format that was named "Javascript object notation"? Oh there is?

parsed = JSON.parse(inputField.value);


You're even using JSON.stringify already...



Other general advice


Don't use classes to identify unique elements. That's exactly not what classes are intended for. Instead use IDs.
Make use of the strict evaluation mode for javascript... "use strict"; 
You could avoid the e.preventDefault if you didn't use a submit button, but a normal button instead or listened to 'onblur'. I personally would prefer the last method the most, possibly combined with an 'onchange' listener with a timeout.
Always put braces around your stuffs, in this case around the throw new Error. This helps avoid bugs when changing the code later.