Lifthrasil: No, the Vanilla cop would detect if someone is Vanilla or has special gifts or interest. I.e. parity cop, neutral roles and vengeful townie would show up as 'not vanilla'
Vengeful is, in it's nature, quite swingy. It is basically a one-shot vigilante that needs to be lynched to get that shot.
So, which parity cop version would you use? A N0 read and then each night investigate one person an get a 'same' or 'different' result to the N0 read? Or read two persons each night and get a 'same' or 'different' read on those two?
I believe the standard result compares to the previous investigation. So a N2 investigation would compare to a N1, while N1 compares to N0. If you have a Roleblocker, then you need to decide what to do if the Parity Cop gets blocked; if their next (unblocked) investigation compares to the null on the block, then the parity cop can be rendered effectively useless very easily (just block them every other nigh or so).
I do agree with Bler that a parity cop needs a N0. Otherwise they won't have any results at all until at least D3, and that's assuming everything else goes well. A lot of games around here tend to end by around D5.
Jumping roles slightly: You'll also need to carefully consider how the Lyncher is supposed to achieve their win. If all they need to do is have their target dead before game over, then it is (probably) pretty easy (assuming the target isn't something like Innocent Child). If they need to hammer, that is significantly harder, and may end up being nearly functionally impossible. Also, if the lyncher achieves their win condition, is the game over? Does the lyncher stay in the game (possibly getting a new objective), or does the lyncher leave the game (possibly ending it unexpectedly)?