Jonathan, yes , I guess you are right in that Strong as they need to be is usually in long action-oriented series. Really, it is only applicable in genres where combat plays a prominent rule, and particularly ones that are based on defining levels of strength and skill. Deus ex machina would really be more universal.
However, I am not sure I agree that Strong as they need to be is a subtrope of deus ex machina, because there are cases where it would not be. Deus ex machina is supposedly only solutions, to begin with, so it could just as well be a form of
diabolos ex machina. I guess that deus and diabolos ex machina follow the same basic pattern, though, so this may just be a nit pick. Also, even when it is not working for evil (which it is not, most of the time, I think), Strong as they need to be does not have to be dealing with an unsolvable problem. It can just be
rule of cool taken a bit far, if not outright taking over.
I am also not sure I'd accept that repeated usage of Strong as they need to be would eliminate deus ex machina. After all, a work can use deus ex machina could also be used repeatedly in a work of fiction. If that standard you mention of requiring there to be no precedent for something to be deus ex machina, wouldn't that make repeated deus ex machina not be deus ex machina, either. That would be paradoxical, if not outright contradictory.
Strong as they need to be is about a character displaying a level of power previously unhinted at, so in the specific case, it is not established. That makes it a sort of deus ex machina, in cases where it is used to solve an unsolvable situation, in my book. Just because the trope has a precedent in the work's writing style, it doesn't change the fact that the specifics of the character's skill and power is not pulled out of thin air. The trope still follows a sort of deus ex machina pattern.
Anyway, I think that Strong as they need to be is frequently a really lame trope, often just as bad and sometimes even worse than deus ex machina.