For 4K I would prefer a PL Cine lens rather than the Nikon. Preferably something fast like the T2 Cooke 15-40 or T2.2 Angenieux 17-80. Or the Red zoom even though it is a stop slower. In any event I would much prefer a PL mount Cine lens. No adapters please! Optics quality is critical at 4K. That would be my vote, although I may well be in the minority.
I know it will be a problem for Gates picking which lens to support. That is why the simplest thing may be to go with the RED Zoom (which is relatively affordable), and then we can get more exotic later. RED camera plus RED zoom plus Gates housing. Makes sense to me.