I mean, yeah, you are 100% correct. if you really want me to dissect the joke, I'll go ahead.
first off, for a joke like this to work you need to achieve suspensions of disbelief. that means staying somewhat in character, not exaggerating too much (I know that is the point, but even with exaggeration there is a sweet spot), staying very true to the original language, perfect mimesis (imitation).
I thought yours was overdone, too over the top, too much "screeching". your parody of an SJW didn't sound like an outraged SJW, it sounded like a parody of an SJW. it sounded like what someone who is really disconnected from twitter/SJWism/the whole political correctness bs would think it would sound like. which made it unfunny.
is that too meta already for you, boy? watch this!
if you allow me to dissect the joke of mine that you quoted, I would also say that it's pretty unfunny. if I hadn't been sleep deprived I prolly wouldn't have posted that, seems a lil contrived in retrospect. my quality control sensors didn't kick in.
it's fundamentally different from your joke, however, as it is a meta-joke: it is a parody that self-identifies as a parody, and implicitly declares itself as a bad parody: a "humble", self depricating joke. but it didn't work. either my parody wasn't bad enough, or I made it too obvious that it's self-deprecating, I ain't sure yet.
yes, I've taken a seminar on how to explain jokes. judge me.