So the issue is with the code. The developers and support will not admit it. Pretty clear they didn't optimize it
No, that is not the case at all. Planet Coaster just relies more heavily on the PCI-E bus than other games. Some games will run just fine on a GPU that is only running at x1, other games will struggle.
At the same time, a stronger GPU will be bottlenecked greatly by running at x1 while a lower end card won't. This is why the game runs just fine on the old R9 270. The R9 270 is not bottlenecked by the x1 slot speed. And, IIRC, Planet Coaster also auto adjusts game settings to match the graphics card, so it will run smoother on the R9 270, because it is automatically turning down some game settings.
The problem is the slot is only allowing graphics cards to run at x1. This is a problem that needs to be fixed, not something to just blame on the developers of the game.
Now, the problem can be a lot of things. Some times it can be a damaged video card, but we already eliminated that possibility by switching cards. Since both cards have the problem, we know it isn't caused by the graphics cards.
That leave a few other possibilities.
The PCI-E slot on the motherboard itself could be damaged. This is hard to test for.
The card might not be going all the way into the slot like it should. OP, I suggest making sure the back tab is clicking into place when you insert the graphics card.
The new CPU could be faulty. The PCI-E lanes are connected directly to the CPU. If the CPU is bad it might not be activating the PCI-E lanes like it should.
The CPU cooler could be over-tightened(if you are using non-stock cooling). I've seen this happen. Again, because the PCI-E lanes are connected to the CPU, if you over-tighten the CPU cooler it can actually cause the motherboard to flex. This causes a bad connection between the CPU and the motherboard, and the PCI-E lanes to not work properly.
My next step would be to put the old CPU back in, with the stock cooler. Then see if you are getting an x16 link with the graphics card. If you are, put the 4970K back in, with the stock cooler, and see if that gives you the x16. If it does, then put your aftermarket cooler back on, if you were using one, but don't tighten it as much.