So, I think I have noticed a pattern with the written accents- if a word is primarily proparoxytone, it becomes secondarily oxytone when followed by a genitive. Is this correct? How would one write "your elephant"? Is it "ο ελέφαντάς σου"?
Yes the possessives are treated as an ending to the noun and the accent cannot be proproparoxytone. In Finnish the possessives are even written together with the noun: koira or σκύλος (dog) , koirani or ο σκύλος μου (my dog)