I have rebuilt many of the original Postwar units. I haven't done any of the reissues, but am somewhat familiar with the construction of the launch mech.
The typical problem with the postwar versions is multiple rockets firing together, which is caused by the foam under the mechanism decaying.
Sounds like the coil isn't pulling in the armature/pawl that rotates the firing cam shaft. Someone else mentioned the problem in the thread you linked. The Postwar one needs a fair amount of power to fire reliably. I've always used fixed voltage to test end operate mine.
There are no Postwar Lionel diagrams for the #44 / #45 missile locos. I think Lionel did something for the modern era ones.
