Depends. Who exactly is doing the work, and how good are they? If you take it to a specialist that knows the car, especially DMCH, that would prove the work done is quality and appropriate. On the other hand, if the work done is not by a competent mechanic, especially one that does more damage than repairing, that might not be the best thing. That's why you should create a solid portfolio of the car if you wish to hold a private sale to ease the buyer's mind.
I'm not going to lie, $3,000 isn't anything to sneeze at. For most of us here, that's a pretty good chunk of change. But it's also pretty damn cheap for you as a way to get into DeLorean ownership. I mean, you have the car already, and it *technically* didn't cost you anything. So it would just be $3K for you to get behind the wheel of a running DMC-12. And of course you can do it at your own pace so that you don't have to spend all that money right now at this minute, let alone all at once. Most of all, if you ever want to get back into DeLorean ownership, it will probably be a very long time before the opportunity for you arises again.
So the first question in reality is: Do you actually want to sell this car?
Now if you're sure you want to, you've got a couple of things to consider for the second question: How do you want to sell the car? Your selling to a business such as DMCH, GCMW, or someone else will indeed alleviate allot of stress off of you. First is going to be the financial burden. Could you get more from a sale by investing cash? Sure. But the real question is if you can, and how much of a hardship would that place upon you? Sure, they're going to flip the car for a profit, but it's non different than what you're considering doing. But just like them, it takes cash, which they have. The second aspect of stress you don't have to deal with are scammers. Once you sell, you have the cash, and they also have all the risk of dealing with scammers and tire kickers. Selling cars on Autotrader, and especially damn Craigslist can be frustrating. But you won't have to deal with that. So in one aspect the price difference in selling is the price you pay for the convenience of not having to deal with all of this.
Now you don't have to answer to anyone here. But I would advise you weigh both your options as well as your desires to see what it is that you really want to do.