So, in that case, I'd say that going with whatever card you can afford that is tiered higher than the current card, so RX 570 or 580, or GTX 1660 (Or super, or TI, if so inclined) would all likely handle any game at Ultra 1080p without struggling too much. Especially on those types of games.
Since the CPU is not really the issue as you say, then all you can do is try it out. Be aware though that once you have a GPU that CAN handle things at a given quality setting, it WILL increase the demand on the CPU and possibly to the point where it then becomes the bigger problem but as long as you're able to get the desired quality setting and eye candy, that might not matter. Besides which, if you already have a card that can handle your desired settings, you can always upgrade the platform later if you need or wish to without having bought the graphics card being any kind of impediment.