You have two feet. Any attemp to wear three shoes will end badly.
I'm the kind of writer who finds starting new projects and exploring new ideas more fun and easy to do, rather than stick to an already estabilished story and finish it through. So, I understand where you're coming from.
My advice here would be to choose what you want to finish first. You mentioned two books: are you writing them at the same time? Would you be willing to prioritize one over the other?
How can I budget my time and keep a regular writing schedule so I can finish the pieces and write them to the best of my ability, without giving too much or too little attention to any one thing?
If you already feel that you are being stretched too thin, you will have to drop something. Not undefinetely, but for a little time. You are not abandoning your projects - you are postponing them until you will have the time and mental energy needed to see them through.
I'd suggest dividing your schedule by thematic areas. You could decide, for instance, that you'll deal with academic writing every odd day and creative writing in the others.
Or you could say, "I will finish my academic writing exercises as top priority, then try to work at least one hour on my creative projects. Anything after that is extra if I feel like it".
I see no issue with dividing academic and creative writing, since those are different enough that they should "drain" different areas of your writing skill, at least partly. I'm also assuming that you can't skip your class, so the academic pieces are mandatory.
You can go as detailed as you want in those schedules. Some writers go with word count, some with time counts, some with no counting at all (sometimes, it's just important to feel that some progress is being made). It's up to you: some people don't work well with tight schedules, while others work best with the so-called "deadline pressure".
Regarding the creative writing, it's fine if sometimes you let it "derail" and write something completely unrelated, like a short story or a character study.
But, again: pause one of your books. Writing one to the end (and then revising it) is already quite a feat. You can (and should) write down your ideas for the other book, along as any other cool concept or plot development that comes to your mind, and storage them for later use. But you'll be more productive if you focus your creative energies on a single target rather than two.
As soon as you finish the first draft for a book you can switch on the other, then come back to revise the draft once you've finished, and so on. That will allow you to write on a single project "at the best of your ability". Creativity is a wonderful thing, but sometime it has to be reined to stay on track.
If you still want to keep all your projects open, you can further divide your schedule. Again, it depends on how much of a schedule-type you are, but something along the lines of "I'm willing to work on project X 4 days a week, while I'm fine with 3 days a week on Y". Honestly, I'd advise against this, because swtiching from a context to another is - well - not effective in my personal experience, but who knows. Every writer is different.