I’d suggest that, given that the problem @Puck_Mendelssohn outlined was “conspiracy theory” getting truncated down to simply “conspiracy”, that your “pseudo-conspiratio” and @swamidass’ “rhetoric of persecution” are likely to endure the same fate, if we managed to insert them into the lexicon in the first place.
“Pseudo-conspiratio” would almost certainly get truncated to “conspiratio”, which is similar enough to “conspiracy” to continue the confusion (and likely the unfamiliar “conspiratio” would eventually morph to the more familiar “conspiracy” in any case). "Rhetoric of persecution” would likely become “persecution”, which has the advantage of moving well away from “conspiracy”, but may yield fresh confusions.
When I was contemplating this question on my walk yesterday, the phrase that I came up with was “Illuminati thinking” (centering it around what is probably the oldest extant conspiracy theory – the Illuminati has been linked by conspiracy theories both to the French Revolution and to the New World Order). This shouldn’t create too much confusion if truncated to simply “Illuminati” – but would cause amusement to those of us who remember the card game of the same name (and similar theme). 