Ok, repeated, this time I made sure the HDMI was unplugged from the NUC while the USB-C cable was in use. It would appear that the HDMI port changes from 00 04 00 00 to 00 08 00 00 in that case (unplugged).
The thing to figure out is why it changes when plugged in.
Will let you know if I have something to try.
I was able to reproduce the connector-type changing to <00 04 00 00> even though it is correctly patched for <00 08 00 00>. It has something to do with the re-arranging of connectors. The ig-platform-id 0x59260002 has an LVDS port as the first connector. Of course, this NUC7 does not have any LVDS, so there are two patches that limit the number of ports from 3 to 2, then moves the @1 and @2 connectors into the @0 and @1 positions.
If you disable those two patches, the HDMI will connect to @1 and connector-type <00 08 00 00> will be honored.
So, try disabling these two patches:
"0x59260002 0x59270004 2xDP, #1 of 2"
"0x59260002 0x59270004 2xDP, #2 of 2"
Then test. You can even temporarily disable the patches via Clover Options -> Binaries patching menu. In ioreg you should see your HDMI connected to @1, connector-type <00 08 00 00>. You will also see the @0 (LVDS) connector in there, but it doesn't seem to cause a problem for us here (on some computers, extra connectors cause strange lags at bootup and wake from sleep).
Report results. Wondering if having the correct (and unchanging when plugged in) connector-type helps with the 4k@60/HDMI problem.