I wouldn't say you're wrong, bt, only that my understanding was that the first false GP can be as low as 6 (maybe 6.5 deg). I'm not among my books at present, so can't follow that up further (but will).
On your other point, it is the same one that others have made on this topic. My answer is "yes, you can x-check against various fixes. And yes, you can immediately tell that you are on a false one, but by then it's too late to recover to the true one, so you have to go round, so it's better to be absolutely certain before you start that you are intercepting the correct one".
Everyone quotes these cross checks will be a certain defence against the false GP, and so they are if everythings going well. But do late/rushed descents no longer happen? My experience in the sim suggests otherwise...