Like many other answers that were already given, I would say that the most recommended course of action is to accept the failing grade and to not fight it.
However, I think the second paragraph you wrote contains quite a bit of logical reasoning that I didn't notice addressed in the other answers. So I wanted to do that as well.
The original poster will not like this information, but enjoyment doesn't equate to accuracy. I believe what is about to be said to be true, even if such information may not be a nice and pleasant experience.
I don’t believe an F is a reflective grade of the knowledge and work that I put into that course
A grade of F does not reflect your knowledge and work you put into the course. However, the grade of F does reflect what happened.
You had very specific instructions, and those instructions were not successfully met. The grade of F does reflect that.
I don’t believe that a student should learn and learn for an entire semester and then have one time slot to prove their knowledge.
Perhaps such a restriction should not exist. However, whether you believe this to be decent or not, the simple reality is that this restriction apparently does exist.
People make mistakes and I need a chance.
Many people would say that what is actually needed is a lesson, even if that lesson is as harsh as lowering a GPA and requiring the repetition of the course.
Understand that many people think of a university as being more than just a place to learn knowledge, or even a place to demonstrate that you can work hard. Many people look at the university experience as a test that evaluates whether you can do what is required, which may include things like passing an unenjoyable course, getting work done on time, being at a specified location when specified, going through any efforts required to sign up for courses and get any required signatures, and any other tasks that the university decided is required.
I need to think of an innovative assignment to turn in after the meeting that may interest her in giving me a few points to pass.
Your instructor may not be easily persuaded. An instructor may have a lot of power to make decisions that affect a grade. This could include making a decision to be rather strict about a specific policy, even if you view the results as very harsh. As much as I may disagree with the decision that your instructor is making, I am an instructor myself and can say that I have found such ability/power to be very useful in many circumstances.
Trying to circumvent a decision is the exact opposite of accepting natural consequences for your actions, which may be the precise lesson that the instructor is hoping to impose upon you. Therefore, demonstrating that you are desperately seeking to avoid such consequences, by any means possible (including newly invented ideas like performing additional work) might serve no purpose except to reinforce the instructor's belief that winning this battle is of paramount importance.
What I can take upon myself to do – even though my professor said there is nothing – to show her that I am willing to put forth the effort and that I am committed to learning.
See, if you demonstrate your ability to put forth effort and be committed to learning, that doesn't necessarily help your case. It only shows that you are trying to invent your own way to try to achieve the goals you desire, and not that you are willing to submit to authority or accept justified consequences.
Does anyone know what I can do?
There is one thing that you said that may provide a key clue...
she couldn’t meet with me unless the head of the department of marketing (her boss) was present.
The instructor has provided you with a recommendation. Arrange a meeting that involves the Marketing department's head/chair.
The meeting is tomorrow at 12:30, after two other finals starting at 8.
Excellent. You have done so already. (And, unfortunately, already had that meeting before this answer was posted.)
Note that even if you miss the scheduled times when other people took their final exams, you could still get a good solution. Some time might be allocated for when you can take the final exam on your own. This might or might not be a decision that some people (who may be rather sympathetic, or might not be) may provide. There might be other consequences too.
Understand that you have the powers to politely request and to hope, but not to demand or insist. Fighting is most likely going to cause you to experience the people who have power in this scenario becoming even more uncooperative, perhaps even in the long term while a class is repeated. A humble approach is much more likely to serve you well, even if the final result is not what you hope for.