This is a HUGE question that needs to be addressed with your doctor right away. I can't give you medical advice about how you should dose a taper, but what I can tell you is that tapering is risky because it puts you into mini withdrawal, with the dope sickness that comes along with it, and since you are still in possession of pills, the tendency for most of us is to "fix" the dope sickness with more pills. It's just too hard for most of us to continue feeling sick when we have the pills in our hot little hands.
Your doc is very wise to have warned you about oxycodone and her concern for putting you on it. You are experiencing why she is worried about that.
What you are experiencing is something called "adaptation", where your body has become accustomed to the drug and no longer gets the same "rush" it gave you when you started. It also doesn't give the same level of pain relief as it did before. If you were going to be on oxycodone/oxycontin long term, the doc would probably respond by upping your dose, changing your opiates around, or changing the method of dose. But since the aim is for you not to be taking opiates, that would be a bad idea in my opinion. Unless you want to be "that minister who uses opiates". Maybe there are a bunch of them, but in my profession there aren't ANY unless they are in hiding.
Fortunately, your dose is still low enough and brief enough to where you will suffer withdrawals but for less time and probably less intensity. The reality of stopping opiates that have been going on for longer than a few DAYS is that most people will suffer withdrawal. When I had both knees replaced in 2009, the orthopedic nurse who was helping me told me that most of her patients had withdrawals and just thought they had come down with the flu for a few days after they quit the drug. Since most people passed it off as that and didn't give it another thought, their office didn't pursue any kind of special program to stop, although the usual method was to taper the patients off between postoperative and 3 weeks after surgery.
My strongest advice to you is "get off the train" before it leaves the station. Opiates are nothing to mess with, and you may be saving yourself months if not years of misery being addicted to a drug you had no intention of abusing. I started out with my surgeries and escalated my use afterwards. If had known then what I know now, I would NEVER have taken opiates after that 3rd postoperative week that MOST people after orthopedic surgery are usually able to do.
You'll get lots of support for quitting opiates on this forum. Good luck!