I actually agree with you about the appointment issue --- in the sense that my guess is that FISC court appointment procedures mean it isn't an Article III court. But a couple problems with that for this line of argument:
* There are Article I courts; Congress is empowered to create tribunals for which the Article III appointment rules don't apply. Since the FISC is adjudicating policies that Congress is already empowered to legislate (the Constitution being as silent on foreign surveillance as it is on the makeup of the Air Force), not adhering to Article III doesn't automatically make the FISC unconstitutional.
* In trying to pursue my leg of this argument over the past couple days, I've been pretty well slapped down on the idea that appointment issues damage the Article III standing of the FISC: