This is my experience. I've quick tapered from an oxy addiction twice, and these methods worked.
1. I went to a doctor that charge about as much as the quote you got for the first doctor, about $1k. I went in, they piss tested me and took my blood and blood pressure. He got a brief history of my psychiatric history (I have a couple of things going on there), and what I was taking and how long, etc. This took about 45 minutes, he was thorough. They gave me a 2mg Subutex to make sure I wouldn't have precipitated withdrawal too bad if I was lying about my last dose (it was about 36 hours after), and then he gave me 16mg of Subutex, I was monitored this whole time, but he had a couch area ands stuff, wasn't too bad. Also my mom was with me, Then he gave me another 16mg. Now I know this sounds weird, but with this dose I didn't have to take another for 2 1/2 days, and I was just a bit sick waiting like the three hours I waited for him to call in the Suboxone (he gave me Subutex in his office, but now it was Suboxone at home), not really bad at all. When I needed more, he called in 2 pills, and it lasted about 2 days, then he called in 1 pill. This process took about 7 days I think, and I saw him on day 4 and day 8. He prescribed me clondine and at this point and an anti-nausea pill, can't remember. I was a tiny bit sick, just insomnia and runny nose, very minor. Then, NO WITHDRAWAL at all at about day 10. It was almost painless, I'd say the worst I got was feeling 90% normal as opposed to 100% normal, on oxy it'd be like 0 - 25% for at least 5 days. I was also high as fuck the whole time on Suboxone, it was actually probably one of the times I was the highest in my life on that 34mg dose, so the insomnia and minor stomach craps were not a big deal at all, I knew the pain was there, but I didn't really feel it.
2. I went to another psychiatrist that my normal psychiatrist recommended. I didn't have insurance at this point, so the fee was 100 dollars per visit (two visits). No blood pressure or piss test or anything. He got a very brief history, and then prescribed me I think 8 8mg pills. He instructed me to take 16mg the first two days, and another half if I needed at night (which I didn't, also clonidine I didn't need). Then it was 8mg for two days, 4 for two days, 2mg one day, 1mg three days, then off. This was not as painless as the first detox, but still it was VERY minor compared to cold turkey. I wasn't high like the first time (probably due to my tolerance being much higher. I didn't really like this doctor, his personality rubbed my the wrong way. I went to him about a year later for maintenance, he was the cheapest doctor by far and after two or three months he started writing me scripts with two refills (plus one script lasted me for way longer cause I was taking less than prescribed after a few months when I realized I didn't need nearly as much as I was taking. He let me detox at any pace I wanted, I was on it about 9 months or so. To get off it, I started spacing my doses so I only took it about every 2 1/2 days (near the end), started with 24 hours then it went to 30, then 36, etc). I jumped off at 2mg when it was getting to 2 1/2 days, and had no withdrawal at all, zero, zip. So he was a nice and fair guy for sure, just rubbed me the wrong way like I said.
Sorry for the long post, but I want to illustrate that it can be close to painless. You could take the smallest amount you can feel decent on, but to me I'd rather not worry and also not suffer for while trying to take such small amounts, even though much smaller amounts than I took would also hold you. Also being high was cool. BTW, I paid about $7.50 a pill when I didn't have insurance. This was at CVS, they were the cheapest out of CVS, Walgreens, Target and Walmart.
Good luck whatever you decide to do.