"Most every Linux deployment to replace Windows has come with higher initial support costs."
But was that caused by Linux or the way the transition has been set up? I think the latter. Thing is: a lot of people allow bias and personal preference to slip in, sometimes right up to a point where it becomes ridiculous. Another important question: in which area did the replacement take place?
We replaced all our Windows (2k3) servers with FreeBSD and yeah: it is absolutely true that the transition itself wasn't free. It took time (which amounts to money), it took re-training of some admins and we also replaced some hardware. Oh; our backup policies also had to be redone because of ZFS.
But I can't recognize our situation in your story at all. We didn't have to deal with higher support costs: our end users didn't even understand what all the commotion in the IT department was all about. They had no clue that they suddenly were using completely different machines. It was just business as usual for them. Some even called us a bit crazy because of it :)
Sure; this becomes different when we're talking desktop replacement, I can see that. But that's not what you said up there. But higher initial support costs per definition? It doesn't have to be that way.