Local computer shops might be a place I’d check. I know some places that could put a high schooler after school to work on a simple project like that for a few days.
I calculated that 4 DVDs per hour would take 250 hours....that's several weeks of work. I found a robot that does this, but the company that makes it seems to have gone out of business.
Assuming a single-threaded process with one final destination, sure. If you're just archiving them, a couple cheap-o machines with external SSDs can really crank through the bytes.
1000 dvds is really not such a large number, it will go a lot quicker than you think.
Source: I once made 180(!) copies of a ~400 page document for an event, by using six copy machines and collating from stacks of 30 sheets. I don't remember exactly how long it took, but it was less than 2 full workdays. It's all about the M:N efficiency!
