Even if the board were not a limiting factor...
If you want to do 4 R9 290's, you are going to need a custom water loop and a 1000w PSU or better. You're talking about MAJOR heat and power specs coming off those cards. You'll easily need 800w just for the GPUs, if not more. You'll also need an overclocked 6 core Intel to even get close to being able to drive all 4 of those GPUs to their full potential, and even then 3 290's is probably the most that CPU could support without bottlenecking.
3 is actually a much better option. It will be better balanced between CPU and GPU powwer. You could get away with an overclocked 4770k, but the CPU will still be the weak link in that chain. Maybe take the money you didn't use for the 4th 290 and put it into the better CPU and cooling?