Well I had thought that it was all a bit of a lost cause earlier that it was slow. Turns out I did manage to get the port working at 5Gbps speeds with the IOPCIMatch rename! To check the speeds on the Asmedia I used BlackMagic SpeedTest with a hard drive instead of a USB 3.1 stick I was using earlier which didn't have too high a result. Surprisingly the USB 3.0 speeds match those on my new Z370 Prime P as well as my 2013 Haswell MacBook Air and there is definitely constant power (no dropouts) so it is partly saved...
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So the kext is here if anyone needs it. At the moment it works only on the bottom port of my P8Z68 V Pro Asmedia. You'll need to combine it with FakePCIID and FakePCIID_XHCIMux as well as a XHCI-200-series-injector. I'm still testing it, but it looks good for now.