The ioh3420 is named root.1. You have the Radeon (01:00.0) attached to it, but the HDMI (01:00.1) is attached to pcie.0, which is the default name of the Q35 Bus. Put it at root.1 too.
Also, the addr for the HDMI has to be at Function 1 of the Radeon.
-device ioh3420,bus=pcie.0,addr=1c.0,multifunction=on,port=1,chassis=1,id=root.1 \
-device vfio-pci,host=01:00.0,bus=root.1,addr=00.0,multifunction=on,romfile=/opt/kvm/images/Sapphire.R9290.4096.140115_1.rom \
-device vfio-pci,host=01:00.1,bus=root.0,addr=00.1 \