It looks like you can connect a replacement! (Assuming you can solder and have some electronic knowledge)
If you can't solder, then it's a useful skill if you do any electronics. However, this project isn't much of a beginner project. If you can't, do you have a friend who thinks they can do it?
I recently stumbled on this post. It shows how one person bought the retina panel used in the iPad and they did a bit of soldering with some adapters, the screen, and a homemade PCB. The parts (including the panel) added up to $70 shipped (not including the PCB, power adapter, a TPS61175 step-up converter, and a few cheap parts that cost only a few dollars.)
The post has the schematics and the instructions. Read to see if you think you can attempt it.
A couple of things: it isn't touchscreen, you would have to build a case for it, and it may have some glare and not look as glossy as a real iPad screen does. For the last problem I mentioned, you might be able to ask a question in the comments about how it looks before you buy anything. The author says that the pictures look nothing like the real thing, but it never hurts to ask. You don't want to get stuck with a monitor that the screen looks old at a glance (one of those that has lots of glare and looks kind of flimsy), even if it is high resolution. I don't know if Apple adds a layer to make it look high quality.
It only supports DisplayPort as an input. Depending on your setup, this may be a problem. However, at only $70 per monitor, you can afford a few extra cables and adapters.
Good luck if you do attempt. If you need any help, you probably could post a few questions on EE.SE. I would offer, but I don't think that I'm that knowledgeable. =)