Max M. answered 12/06/19
Harvard Literature major with 20 years of coaching writers
Interesting! And it does sound a bit tricky given everything you've laid out. One quick question: are you hung up on the American-ness of the Beat movement? Is that its most important quality? If you look beyond that, are you still just as sure Things Fall Apart doesn't follow it? If it's not just that:
My first thought is to frame your arguments around rebutting counter-arguments. Are there connections someone *might* make between Beat literature and Things Fall Apart, and if so, what are those connections missing? In other words, why is it even an interesting question to read Achebe in the context of Beat lit, especially if Achebe isn't a Beat author? I'm not asking that rhetorically--if you take that question as your essay prompt, do more ideas start to come?
Another, slightly drier option might be to approach it as a compare-and-contrast. What are the essential qualities of Beat as you see them? Then, what does Achebe do on those axes? E.g., let's say you argue that the prevailing emotional tone of Beat lit is disaffection. What, then, is the prevailing emotional tone of Things Fall Apart? Do that for as many paragraphs as you need.
Lastly, depending on how your prof reacts to such experiments, you might try writing a devil's advocate paper. In other words, try to argue that Things Fall Apart *is* a Beat novel. Normally I discourage students from writing stuff they don't believe, but taking the opposite position can be an interesting thought exercise, so if your prof is open to it, you might give it a go.
Hope this helps, and happy writing!