Wow, thanks for clearing me up on this. I wasn't aware that such cases existed.
As Multifinder17 notes above, it can't hurt to ask.
You could also get the parts yourself and open up the new machine. You can get the official Apple double-sided tape for the display fairly cheaply.
However, if you get AppleCare on your replacement machine you may not want to do that. I'm waiting until the coverage runs out on my own before opening it up but I do plan on replacing the 1TB Fusion Drive with a 1TB SSD only after that. I figure the prices have to have come down by then.