Methadone isn't a good pain option either when used once daily, which is what you'll get at a clinic. It needs to be dosed every 4 hours for pain. It's also just so much more potent than what the OP is on.
Yeah, I felt well when I was initially on methadone but I was an IV heroin addict at that point and years past the point where oxycodone had any effect on me. Even at over 1000mg doses. On methadone I felt tired, depressed, and had no appetite on methadone and my side effects were minor compared to most. Took me well over 6 months to taper off a high dose and that was on a pretty fast taper plan... one that I fought my clinic for every damn week, they really have no interest in helping you get off.
To sum it up, using methadone to treat OP's habit would be like using a sledgehammer to crack a nut. You wouldn't feel normal, you'd feel high. It would jack up your tolerance and clinics seldom do rapid detox and even if they did you'd still get WD symptoms. You're better off tapering your own medication than getting on methadone and tapering off.
You need to try the easier options before going straight to the most extreme course of action. I would first get back on your prescribed amount only. Then you could request that your doctor taper you off by slowly lowering the amount prescribed and also scripting medications to help with withdrawal symptoms. Something for sleep and anxiety would be ideal. You could also try checking into a 5 day detox, it's cold turkey but you'll get benzos and other medications to treat withdrawal and it's not our of the realm of possibility for your habit. If those suggestions are just not an option, try and find someone you can buy buprenorphine off of, it's usually around. Get enough for a week taper.
Treating the causes of your addiction is important too, whether it's treatment, therapy, meetings, etc.
Question though, how severe are your pain issues? Can they be addresses with physical therapy and non-narcotic meds possibly? I will tell you right now, if you go to a methadone clinic or get buprenorphine scripted you'll never get opioids for pain again.