I've tried to look for how you are preventing duplicate accounts and answers didn't make sense to me, but as you said in here:
Proof of person is based on the Turing test running at the same time for all participants in the network.
I feel stupid for not getting this but i have to ask. Does this mean that every user needs to be online solving the test at the same time in order to participate? It's the only semi-reasonable answer i am getting from this, even though it doesn't sound plausible or even reasonable. Please tell be i have been mistaken.