Tristan, as others have noted, your cage as described is legal.
HOWEVER, your goal is to finish your school, and every once in a long while you'll come across a tech inspector that can be a real a**hole and do their best to ruin your day (disclosure: I'm a Divisional Tech Inspector. I know the attitudes because it was due to the pigheaded - and COMPLETELY wrong - attitude of one of them that I volunteered.)
Here's what you want to do: find out who your regional or Divisional Chief of Tech is, and bring your car to them for an annual inspection IN ADVANCE OF THE EVENT. Once you've been issued a logbook and it's been signed off for annual, you will not have to present your car for the event itself.
I CANNOT stress enough that you want to get this taken care of in advance of the event. Theoretically, if you get any grief over the cage you can file a protest against the official(s), and eventually it will be found in your favor. However, you do *not* have the time or motivation to deal with this the day of the event. - GA