hey Kerra.
i know how parents are with pets,just stubborn.
did you tell them YOUR arguments? your side of the story? try convincing them into getting you a cat. like you said,you will pay it...then you might add that only you will take care of her,you wont let her out of your sight,you wont let her get near them and you will clean her and after her.
i dont get what your stepdad's music studio has to do with a cat. not like a small creature can destroy it.
if you dont travel as much as they do,you can keep the cat. more people just leave their pets at neighbours house to take care of 'em while going away,or bringing them along if its allowed,like in a backpack.
and tell them that thats all you need,you wont bother about anything after you get a cat.
did you ever had an argument of your own against their thoughts about this? i just made an example,you gotta be careful with how you speak to them. not too mad.
and if this turns down anyways,you can always get a cat when your 18 and alone. it shouldnt be much of a problem. just be patient.
i wish you luck at it overall. hope things go great. just show your responsible.