I'm going to take a different take. First I'll answer your questions.
Will a 970 work well with your resolution? Yes, absolutely. It's very much overkill.
Will you get good performance? In what way? Graphically? Yes.
Will you be bottlenecked? Yes, but it won't be relevant at that resolution. You'll get more than enough fps to have nice looking gaming. Instead of spending money on a new mobo/cpu or just a cpu. Sink you money into a nice new monitor. After all, you have to look at it all the time you use the computer. You won't be staring at the nice new mobo and cpu, right? If you have the chipset and mobo, you could upgrade to this
https://pcpartpicker.com/part/intel-cpu-bx80637i53570k or this...