The Oculus Rift supposedly made that possible in one of the latest versions. But I'm curious why you strain your neck looking at a monitor and wouldn't looking at a virtual monitor. Don't you just need to adjust the monitor physical location to whatever the virtual location you would use?

That's easier said than done. I don't know the requirements of the person you're replying to, but it can be things like needing to lie in bed with screen fairly directly above you, or it can be that the physically constants of your space limit the positions that a monitor can be placed in.