iMac Display Replacment
I would go back to the Apple store to speak with a technician again. Apple repair service has historically been warranted for 90 days or the remainder of the existing coverage (one year or three from original purchase if you have AppleCare) so if you are outside the first year the numbers don't add up. It should be written on the back of the quote they provided you. They might even give you some options for other local service providers that have passed the hardware repair tests to work on Macs but you can always look them up yourself.

The internal LCD panels for that model are integrated with a frame, and a driver board so you're not just buying a commodity 24" LCD panel. You are also buying expertise in case it's not the LCD panel but a video card or the cable. I don't know of many shops that can beat Apple's current labor rates of $39 so you would hope to get a good feeling about why the shop can beat apple's price so much on parts. I always feel better when a shop can explain to me why the parts they use are cheaper than the manufacturer's parts so I can make a good decision.

It's not as hard a repair as say the graphics card or the logic board in that model, but you'll find lower labor rates and better parts prices from shops that do a high volume of that model repair.

Once you've got some quotes you can make a better call in your situation - it might make sense to buy an external monitor even if it's more costly that the repair - especially if that investment will carry forward to an eventual new mac.