Erat999,
in first part I would like to address your question of new CPU, in your case upgrading means getting a new motherboard and possibly ram as well. upgrading to a used 4th gen is an option, to which you will quickly come to realize because of the market, the cost of a 4th gen cpu, motherboard and ram, equals buying a 6th gen new CPU, Motherboard and ram, it all about economics at this point.
but there is light in the tunnel.
considering possible issues; The Witcher 3: Wild Hunt Recommended Requirements
CPU: Intel CPU Core i7 3770 3.4 GHz / AMD CPU AMD FX-8350 4 GHz
RAM: 8 GB
OS: 64-bit Windows 7 or 64-bit Windows 8 (8.1)
Video Card: Nvidia GPU GeForce GTX 770 / AMD GPU Radeon R9 290
I would ask how much RAM does your system, have, as your MSI 970 unless its overheating (speak about that later, should handle this game just fine.)
Can you get HWINFO program from web, and run HWINFO in the background, then run game for 30 mins normally go in the wild go in the areas it makes your FPS go low. then quit game and look for USAGE and Temps, I am trying to see if your CPU was pegged at 100% usage and how is the video card usage is ? also see the temperatures of the CPU and GPU (max reading) because either being to warm will make them throttle and rob you of graphics FPS.
also do you know what motherboard you are using? maybe the option is to upgrade as far as possible the cpu on this board, if economically making sense, I could see an I7-950 or high could be a improvement, and depending on motherboard, we could consider possibly overclocking your
I7-920 CPU to 4.GHZ
waiting for you to report news.