Whatever it takes, make a good defensive posture second nature (hands up, elbows guarding body, chin tucked, etc.) The Sweet Science. Many things you have to be doing with your body to be a good boxer. That's what I find so intriguing, to practice till these fundamentals are automatic. All the different combinations you can put together to work for you on one guy at one point in time. But it can be pretty tough to start out.
I once submitted my info for application to a Toughman and had the same concerns as you. I have never had good boxing skills (poor footwork and defensive movement, bad timing of punches) and worried about getting beat when limited to boxing rules when it could be a completely different outcome doing whatever we want. But...it is a sport, a competition. The nature of combat sports makes the emotions of winning and losing extreme, but it is just boxing. Just a game. Recreation and entertainment (in this context, don't get me wrong). Not life and death combat.
I think you will do just fine if your training is good. I would just try to remove any passion or thought of it being a 'fight' as opposed to boxing match, and your instinctive reactions will not come so freely. The hard part will be sticking to what is allowed, if you get into trouble. In sparring have your people really put the pressure on, have them come in fresh when you're dead, and have them go all out. Then you'll see whether or not you'll kick or bodyslam or whatever to your opponent that night.
By March you could/should make a huge amount of progress. Best of luck.
Oh for conditioning, traditional cardio and calisthenics, later, intervals. Also farther down the road once you have developed your skills, plyometrics would be a good thing to boost explosiveness and handspeed.And there are other little tricks like sledgehammer training. But for now concentrate on boxing correctly first and foremost. Like I said compared to other things you could learn, this is a lot to to take in at once.
Maybe you could keep a journal on your preparation for this bout. I would definately like to read it and follow your progress.