Welcome to the boards.
Yes tapering definitely helps, the less you've been taking recently when you quit, the less bad the w/d's will be.
I don't want to give medical advice, but provided you take the same amount of milligrams, you're better off taking the oxycontin than the quick-release oxycodone. It's the exact same drug, but it's time-release so you won't be flooding your system all at once with the drug every time you take it. Maybe your doc would switch you to OC20's instead of 40's?
If I were you since you're doing well with your weaning I'd shoot for keeping up the wean, trying to get down to 10-20mg/day, then quitting when you get some time off school for the winter break. Get yourself off to a great start to the New Year
It takes about 7 days to get back to feeling about 90% normal when you kick a good-sized opioid habit. With oxy's, days 2-5 off of the stuff are definitely pretty unpleasant. Beyond day 7 there's usually some mild lingering effects that last about another 3 weeks, nothing too serious ... the fact that you're so young will definitely help reduce the length and severity of the whole w/d experience.
Good luck, and keep posting ...