@ Husar: Yeah, like I said, it's highly contrived. I'm just trying to get at the structure, here.
@ Ser Clegane: Interesting. So Der Euro wird eingeführt worden sein müssen would be okay? This isn't going to be as easy as I hoped, then, because that doesn't quite fit with the apparent ordering I'm seeing from other sentences. My German text has the example sentence Ein neues Ausländergesetz hat eingeführt werden müssen (is this a mistake?). This suggests that the perfective haben (or sein) is higher in the structure than the modal müssen, which is in turn higher than the passive werden. But in your example sentence, the modal müssen is higher than the perfective sein. I thought I had it nailed down as future higher than perfect higher than modal higher than passive, but now it looks like it's more complicated than that. I'll have to see if I can come up with another hypothesis and test before getting back to this. Just to double-check, if we put it in a subordinate clause does it still come out right?

Er sagte, dass der Euro eingeführt worden sein müssen werde

Ajax