no as i said just change HDMI to Deep Color and you will have 10bit like with DP1.2 over USB-C
Here you can see this in the manual.
What i mean is that both HDMI or DP will use compression for 10Bit.
You need DP 1.4 or HDMI 2.0b for 10bit without compression but your monitor doesn't have any of that.
So USB-C or HDMI makes no difference. And with the original Apple USB-C to HDMI Adapter its nearly no difference to usb-c over DP because you will have full Power Delivery as well with your original power adapter pluggend into the adapter and you have at least one usb-a port free.