I have seen the script for the film that became "Cloverfield 3" and all I can say is I hope it was considerably reworked.
There are and have been many attempts at a new Friday the 13th over the last couple years. The one I absolutely loved - from Nick Antosca, a writer for the Hannibal TV series and the co-creator of SyFy's Channel Zero anthology series - was part Richard Linklater-style hangout/coming of age piece, and takes a long time to build characters carefully and then begin to kill them unpredictably. It's funny and sweet and also very dark and violent and unsettling, and it's unlike any other film in the franchise. That got rejected.
There's also a draft I saw from the writer of Prisoners which basically tries to fuse both prequel material (with the Voorhees family) and the first two F13s all into one new movie, which I find rushed and too much. So F13 is back in dev hell at the moment.