the routers I have used don't offer static dhcp but do offer the facility to set a static ip.
It's also a problem I don't have this problem. Not that this matters as some others may find it interesting.
I've never had a router that didn't offer it in one form or another. I'd tried to avoid a term such as "static dhcp" since I felt it might confuse the issue (or even be a contradiction in terms ) but I just checked on my router and they call it "static IP mapping" (even though to the rest of the network they are serving it as dhcp) so there you go.
Just to be clear: I was responding to a specific point that you raised – as quoted in my first post. I'm aware it wasn't answering your original problem. I hope you get that solved …. it's an interesting problem. I have a feeling in the back of my mind that you need a network bridge device but I don't know enough about those to be sure or offer any significant help.