(If you start a site like this, you surely can count on that somebody will be after you. Host it in different country, pay with Bitcoin, hide your registrar data etc so they cannot sue you. If you cannot guarantee it, why start it?)
I think you misunderstand what 12ft.io's business model is -- they didn't bend over for the NYT, the NYT bent over for 12ft.io by paying them to exclude them from the service. Literally the whole point is to extort money from publications to get on the whitelist.