Oh sorry. Didn't realize you did not have the cash to cover the extra. So yes, private party will save you money in the long term, but if you do not have cash to cover the gap; your best bet is in adding it in.
You can negotiate on what carmax gives you. Let me pull up the Galves auto auction value. I was car shopping and bought a months of Glaves, which tracks what vehicles sell for at auction. Was right on the money and saved me a ton of money.
If you want an uber accurate auction quote, give me the trim and mileage. We can see if carmax is lowballing, and if you can bump them up.
Honestly, the degree of rust matters. If they are offering you 9k, I think you could negotiate up. Carmax doesn't negotiate on the new car price, but they will on the trade in value. So, it can help cover the distance for you.
Also. Try other dealers. Normal dealers will negotiate BOTH. I hate carmax by the by. Negotiating is part of the deal. It can be fun if you are willing to walk away. Find yourself 3 or 4 cars..... all with similar miles and what you want. Tell yourself you would be happy with any of them.. that why, when you are negotiating, you can walk away.
As a little proof. I walked away 1 month ago with a 2005 v8 4runner Sports Edition in excellent condition. New tires. 100k, just had pump and timing belt done for 12.4. I got him as LOW as he could honestly go. I know that at auction it sold for about 10.8 to 11.4, meaning I got him down to bare bottom. I wanted him to make a profit to stay in business, just not much of one. He, fyi, listed it at 15k, which is around what blue book is.
Never pay blue book.

Always look at what auction is and work up. If a car sold is selling at auction for 11k, start at 11.5k and work up. Not down from theirs.
Carmax preys on people scared of negotiating. Blah! The first time cur buying, negotiating is a bit nerve wrecking.. but it is kinda a trophy to adulthood.
Anyway. If you get me your vehicle specifics and maybe some undercarraige photos, I can hook you up with a decent auction price. Auction price is what dealers sell cars to each other for.... so, it helps you figure out how low you might be able to go.