Static IP address?
Is it just me, or is that not the obvious workaround?
Skip DHCP altogether and set up a static IP address for the machine - you can do that in Windows, can't you?
The only piece of information you need to do that is the network address block - in most home routers that's likely to be 192.168.1.0/24 - and then choose any one of the mid-range numbers for the last octet to avoid conflict with the router and other dynamically-assigned addresses that might be in use.
I have quite a few devices on my home network and for me it's helpful to know the IP addresses of some of them (I have a raspi to do my internal DNS). The mobile phones are about the only thing that use DHCP in here...