No matter how much someone is willing to give up in order to have this technology (or anything they want badly enough), they can not give what they don't have.
If there is no insurance to cover the costs, and no grants (or you've already factored these in), then you're left with down payment and costs of a loan.
The payment may have to be made all at once (like it is when you buy a house) but banks will eagerly step in provide financing to qualified borrowers.
When you buy a house you either pay "all cash" (which means you just buy it outright, not necessarily literally with cash) or you get a mortgage. In the US, a standard mortgage is fixed rate for 30 years. Interest rates are relatively low (right now they're in the 4% range) but, when you pay over 30 years, you end up paying more in interest than in principal. Most banks will only loan you money for a single-family home such that the maximum monthly payment is no more than 1/3 of your income. You can fudge that some, but the understanding is that's what is reasonable for most people to pay.
If a new body were a house, we could calculate an amount that >60% of the middle class could not afford to pay off.
But a new body isn't a house. What's the difference? If you keep a house in good condition, it will still be worth about the same amount in 30 years (barring changes in the market, inflation, and the drop for a brand-new house).
Your new body is worthless to anyone but you in 30 years. It may even be worthless in 30 days. We don't know if the technology (or ethics) exists in the author's world to "repossess" a body and sell it to someone else. Even if it does, that body will age.
The reason banks are eager to make loans for people to buy housing, if there is a reasonable chance they'll be able to pay it off, is because, if the borrower fails, the bank gets the house. They get to sell it and take the first part of the profits to pay the loan and their costs. If there's anything leftover, the former homeowner gets it. Or the homeowners can sell the house themselves to avoid the bank doing it. Either way, the loan gets paid (one hopes) from the proceeds of the sale.
You can't do this with a body.
So the question becomes, does the person getting a new body have enough collateral? Their house equity would be number one here.
If you want to prevent the majority of the middle class from being able to afford a new body, set the price so that every middle class family can afford one.
Emphasis on one.
My assumption is that most middle class families own a house. Obviously this is completely false. It used to be true for most though and I'm going to run numbers as if it still were. Assume if you're middle class you probably live in the house you own with your spouse (or that your parents own, or you might be single and own one).
Assume that it is possible to get a loan for a new body based on your home as collateral.
Most households could afford one new body this way. They could not afford two. But most households have two people of about the same age, plus kids. Any one can get a terrible disease or be in an accident. But most people will get new bodies when they get old (which gives you a higher risk of cancer, heart disease, diabetes, stroke, and so on). And most households will have two people getting old about the same time.
This gives you about 60% of people in the middle class who can not afford a new body.
People who don't own homes or other assets that allow them to get loans, and who don't have enough income to buy a house, will be left out.
People whose spouse already got a new body are left out.
People with a kid or a parent who already got a new body are left out. Most kids will grow up, get jobs, marry, and buy their own house. But there will still be enough family members who don't do this, or who get ill/injured young, that it will lower the percentage of middle class people who have a chance at a new body.
Conclusion: Set the price of a new body to around the price of a house in a strong housing market.
You want the cost to be something a family can only do once (families can change houses but not buy more than one at a time, if they're middle class). Getting a new body means giving up your house or using your house as collateral with the hopes that you can somehow scrape together the payments. Very few middle class families can do this more than once. Larger families could, but the numbers still work out because most of the family members couldn't do it.
New homeowners couldn't get a new body because they don't have enough equity. The bank that holds the mortgage gets dibs on the collateral should the family default on payments. Using your house as collateral is ideal for elderly people; the most common customer in need of a new body.