No clue what you guys are doing.
I'm running an olderish 1231v3 with GTX1070, and I have no problem reaching 60FPS in ACC, with details set medium to high, and "visible cars" (not sure what's the correct setting ingame, and I currently not at home) reduced to eight. The only problem is Nurbs, where I have a lot of framedrops too.
AC I'm able to set 34 other cars on the grid at the Nords, with occasional, very occasional CPU warnings. And the R5 1600 has pretty the same singlecore performance as my 1231v3.
My GPU is always running at 50-70%, while locked at 75FPS at FullHD, disabled ExtraFX though, which is very heavy. To run a triple system you'll have to reduce graphics a lot, even if you'd upgrade to a newer CPU. Could you plz check your video settings in CM for me? Afair the rendering frequency of the reflections is set to six faces per frame stock. Not really sure, its been a while since I made changes there. But one face per frame is sufficient, and this should boost your FPS rate. Give it a shot.
If I would have to decide between a 7700K and a 3700x, I'd personally take the 3700x. Both singlecore and multicore performance are higher