Ah, The Power of Cheese also had a lot more bad translation and developmental weaknesses in storyline. It was fun to mock because everybody felt the same way. The writer (was it necro?) simply (i'm sure it wasn't "simple") put into words the atrocious humor that ravaged the game.

FF1 is different. Certainly no great game in terms of dialogue and plot; however, that's more because of missing information than because of bad writing and trite development.
I would treat this assignment as a chance to engage in humor yes, but also an opportunity to creatively design the plot within it's vast, acceptable boundaries. Final Fantasy is about as open for your imagination as you will ever find in a constructed world. It doesn't have to be stupid to be funny, and with only cynical assault on it's weaknesses, I think you will run out of steam fairly quickly.

In short, I believe this can be a much greater imaginative project than Cheese.
I am excited to see what all comes of it.