I don't know if it would be possible to find a nem that will absolutely not move around. I think they all will if they find it necessary.
My H. crispa is pretty stationary. It only moves when it's irritated by the flow of the skimmer picking up. We just did some reworking of the tank last night and we now have a sump, so the skimmer shouldn't be causing any more problems -yeah!
We try to keep ours in an area of flow that it likes, keep it fed, and keep the lighting good and it seems to stay put. Like I said, it seems to be the flow that makes it move most often, and even those moves have only been a couple inches forward and then back. We don't have much coral on that side of the tank because of the nem.
Unfortunately, these guys are horrible shippers and in the midwest, it's hard to find one that isn't incredibly stressed and/or unhealthy. It is possible for them to recover with good care, but it's also possible that they'll disolve in your tank leaving you with a yucky mess.
You've got a carpet so you've got some nem experience, but I would definately check out all your options in depth before deciding so you know what to expect with the one you choose.
Good luck!