I think the simplest way (assuming Windows) for myself would be set static routing on windows on seperate network.
E.g
Type into cmd
route print
Currently all connection that is aimed within my 192.168.0.0(My LAN) network will be sent via whatever interface that ends with 192.168.0.102 (my ethernet)
So to achieve what you want by seperating network access on both computer,
set on cmd:
route ADD 192.168.x.0 MASK 255.255.255.0 x.x.x.x
192.168.x.x being your network ip (usually one before router ip. assuming its a default home router setup)
If router ip is 192.168.1.1 then 192.168.1.0
if its 192.168.0.1 then 192.168.0.0
If it 192.168.100.1 then 192.168.100.0
x.x.x.x is the CURRENT PC's ETHERNET IP
THE MOST EASIEST METHOD if your router supports it (and wifi will be ONLY USED for internet connection isolated from LAN)
turn on WiFi Isolation feature if your wifi router/access point supports it.
This will hide your other PC from Wifi network and force the windows to file share over LAN.
EDIT: expanding on Windows solution, another approach is maybe look into VLAN if you have Intel for ethernet and your router supports routing VLAN tagged packets.
All these might not sound casual-friendly so to speak but seperating two network interface for different access on Windows leans on power user than casual.
I truly hope you don't have to tinker with static route and settle with hardware solution
If you mess up and computer doesn't connect
route /f
will clear all relevant route and reboot to reset back to how it was before you started tinkering with it.
look into EDID emulator to keep the window think there is still HDMI output device being connected.
I don't how EDID emulator works with different HDMI version but that would be the easiest hardware solution.
I don't have the mobo but maybe the no-rollback flag was turned on the version?
Manufacturers make the bios update which makes download/rollback not possible for either the update made changes where rollback would brick the mobo or it was security update which would make the mobo vulnerable again if it was downgraded.
But I don't have the mobo but thats my guess(it could purely be other reasons)
I was watching the latest WAN show and linus and slick were LinusCableRageTip and talking about the e-watch business...
WHAT IF
Someone released wireless charging mouse pad for a wireless mouse so we never have to deal with the MOUSE CORD also the problem of mouse dying out is no problem with battery that never dies out